Show that (p ∧ q) → r and (p → r) ∧ (q → r) are not logically equivalent. Macauley (Clemson) Lecture 2. This is the question: Let us look at the language TAUTOLOGY: Collect all the phrases φ so that each placement on the variables φ will provide φ. Save $25. 0. TUFTOLOGY® is a Virginia-based company and is one of the first tufting suppliers in the US. DirectTautology. This is an invalid argument, since there are, at least in parts of the world, men who are married to other men, so the premise not insufficient to imply the conclusion. The term "tautology" is used in reference to redundancies of propositional logic as well as rhetorical tautologies. p p p p) ( ( p) p) ( ( p) p) ( p q) ≡ p ∨ q. The difference is that tautologies typically use only one or two extra words. Logical tautology occurs when you state something true in all circumstances. Tautology: We are unified--one group, standing together! In this example, the repetition just says “we are unified” in more words. Other semantics for logical truth include model theory, category theory and various kinds of. And so the full statement is the same as the statement p → (q ∧ r) p → ( q ∧ r) because p → (q ∧ r) p → ( q ∧ r) is the same as p¯¯¯ ∨ (q ∧ r) p ¯ ∨. Tufting. We are not saying that p p is equal to q q. In the 1970’s the new generation of philosophers of biology offered a different solution to the tautology problem in two steps. It’s boring cos it is. Some arguments are better analyzed using truth tables. A proposition that is neither a tautology nor a contradiction is called a contingency. It just means that the same thing is repeated twice using different words. "Either the ball is red, or the ball is not red," to use a less complex illustration. 4. For better or worse. The word tautology comes from the Greek word tauto and Late Latin tautologia. This example is taken from Versatile Mathematics, an OER textbook created at Frederick Community College. Ludwig Wittgenstein developed the term in 1921 to allude to. It is not a tautology of intuitionistic logic, for example. Is this a tautology because both last column matches and are. A tautology is an expression of the same thing twice. The bi-conditional statement A⇔B is a tautology. Here are several exercises related to the equivalence of propositional for-mulas. Tautology, in logic, a statement so framed that it cannot be denied without inconsistency. To push further the boundary of examinable logic circuits, it is important to study new efficient checking methodologies. 1. A cliché is a phrase or idea that has become a “universal” device to describe abstract concepts such as time ( Better Late Than Never ), anger. The word ‘tauto’ means ‘same’ and ‘logy’ means ‘science’. Factor the left side and multiply the right-hand side by 1 = n+2 n+2 1 = n + 2 n + 2:Laycock’s statement is based on the first principle of the 10 principles of the theory of ‘crime settings’ by Felson and Clarke (1998): “Opportunities play a role in causing all crime. Metonymy is a literary device wherein one word is replaced with a closely related word. It means it contains the only T in the final column of its truth table. Bringing the best high quality tufting supplies with competitive pricing. Cara melengkapi tabel kebenaran dilakukan dengan menyesuaikan aturan bernalar dari operator logika matematika. o. Namely, p and q arelogically equivalentif p $ q is a tautology. If p is a tautology, it is written |=p. As the name suggests propositional logic is a branch of mathematical logic which studies the relationships between propositions (or statements, sentences, assertions) taken as a whole,. “I love Tetris,” I say. A truth table lists all the possible combinations of truth values for the simple statements in a compound proposition. Concise: We won’t be returning to. Hayder Ghani. Solution: Make the truth table of. 99 $275. Rare. A proposition that is neither a tautology nor a contradiction is called. Problems on Tautology. Tuftology Rewards program, TUFT MORE AND EARN MORE. Any argument with a tautology as the conclusion is valid, no matter what the premises are. In other words, a contradiction is false for every assignment of truth values to its simple components. Tautology is stating the same thing twice in a redundant way, and thus actually takes away from the power of the word or argument being repeated. Common Examples of TautologyScientific explanations are expected to draw upon scientific concepts and natural processes/mechanisms. In grammar, a tautology is a redundancy , in particular, the needless repetition of an idea using different words. Definition of Cliché. Tautology or not, mathematics is useful for expressing and gaining knowledge about the world we live in. Examples: (P _Q) ,:(:P ^:Q) P _Q_(:P ^:Q) (P )Q)_(Q )P) It’s necessarily true that if elephants are pink then the moon is made of green cheese or if the moon is made of green cheese, then elephants are pink. Therefore, If the column beneath the main operator has truth values that are all true, then the compound proposition is a tautology and the statement is logically true. This summary of the weather is an example of tautology because it is unnecessary. job counselor] What are you doing? (breathing) Any questions? (tennis balls) Topics to be covered14. Moreover, saying that it is a tautology is like saying that since the all fish consists of cells, ichthyology can be reduced to cytology, which, in turn, can be reduced to chemistry. Then, (P→R)qualifies as a false, and so does (Q→R). A. Is the proposition (p ∧¬ c) is a contradiction? MSU/CSE 260 Fall 2009 4 Proof Methods h1 ∧h2 ∧… ∧hn ⇒c ? Let p = h1 ∧h2 ∧… ∧hn. The same goes for mathematical propositions. Asst Prof. This can be used in logic statements (or logos), as well as mathematical expressions as a logical connector. Often, a tautology describes something as itself. ”tautology contradiction contingencyAbout the tautological implication. Weight: 3 lbs (1. 00 Save $21. 4: Tautologies and contradictions is shared under a GNU Free Documentation License 1. In fact, it is equally true that "If the moon is made of cheese. Tautology. The types of tautology are verbal tautology and logical tautology. This means that statements A and B are logically equivalent. They are especially important to logic, though. 4. What is the relation between the following claims:In propositional logic, a tautology is a proposition that is true by virtue of its truth-functional form. , you do not need to go so far when you can use deMorgan's rule on the second half of the statement. O A. " In other words, a contradiction is false fortautology翻譯：同義反覆;冗詞，贅述。了解更多。A tautology is a statement that repeats an idea, using synonymous or nearly synonymous words, phrases, or morphemes. Boys will be Boys! Logical Tautology is a single proposition, not a conclusion, though it sometimes looks like simplest case of circular reasoning. Repetition of the same sense is tautology. Are there better ways of telling if a formula is a tautology than trying all possible truth assignments. Like any other healthy entity, it also moves most swiftly without extra weight. From the perspective of model theory, it is convenient to consider "tautology" to be a syntactical concept, because it's a matter of the shape (so to say) of a formula, and not on how the formula's meaning relates to a model at all. But truth is not a proof. Buy them now and get set to be the best rug tufter you can be! 33. If your preferred semantics of logical truth is 'true in all possible worlds' then yes, a tautology is true in all possible worlds and hence necessarily true. This is an invalid argument, since there are, at least in parts of the world, men who are married to other men, so the premise not insufficient to imply the conclusion. , in a way that is not necessary. We can also simplify statements in predicate logic using our rules for passing negations over quantifiers, and then applying propositional logical equivalence to the “inside” propositional part. Often, a tautology describes something as itself. Now, let’s see the Choices of the question:A tautology, by definition, is a statement that can be derived from no premises: it is always true. is a contradiction. A tautology is a compound assertion that is true for all possible values of the separate statements. The opposite of a tautology is a contradiction, a formula which is "always false". Make a Truth Table showing Modus Ponens is a valid argument. tuftology. It is tautology to say, "Forward Planning". Your proof is correct, though steps 4 and 6 are repeated. 3. p ∧ [q ∧ (p ∨ q)] b. The statement (p) ->(qV-p) is a self-contradiction C. ”. a. tautological definition: 1. Мы поможем вам скачать и установить TUFTOLOGY на вашем компьютере в 4 простых шага ниже: Загрузить эмулятор приложения AndriodCOT 3100 Discrete Mathematics Homework 1 Key February 5, 2010 Problem 1 Section 1. If you wanted to be more pedantic (which is always fun), the idea that you can prove a tautology without any axioms is a bit fun to tug on. First, they began by arguing that fitness is a supervenient property of organisms: the fitness of each particular. Let’s look at what makes tautology. Milne. Therefore, we conclude that p ~p is a tautology. Definition of Logical Equivalence Formally, Two propositions and are said to be logically equivalent if is a Tautology. Contingency. Learn more. Featuring an improved design over its predecessor the ZQ-II, this is an industrial-grade tufting machine. "P or not P" is a tautology of classical logic, but not of all logics. Logic and its symbols are very important in tautology. I'll do the first one (I've taken commutativity and associativity as given to keep the proof short): egin{align*} ((p o q) land eg q) o eg p &equiv eg (( eg p lor q) land eg q) lor eg p & extsf{Implication Law} &equiv eg ( eg p lor q. This may seem like a silly thing to prove, but it is essentially the crux of all mathematical proof. Tautology. Therefore the theorem is true. ”. ”. The book can be found at checking is a task surfing the edge of today’s computing capabilities. If they were built on statements that could be false, there would be exceptions to mathematical rules. 2) if and only if p ⇔ q p ⇔ q is a tautology. An example is "x=y or x≠y". 恒真式（こうしんしき、トートロジー、英: tautology 、ギリシャ語の ταυτο 「同じ」に由来）とは論理学の用語で、「aならば aである (a → a) 」「aである、または、aでない (a ∨ ￢a)」のように、そこに含まれる命題変数の真理値、あるいは解釈に関わらず常に真となる論理式である。2. In rhetoric and logic, a tautology is a statement that is unconditionally true by virtue of its form alone--for example, "You're either lying or. Farhan MeerUpskill and get Placements with. 1: Chapter 8: The Logic of Conditionals. When we are looking to evaluate a single claim, it can often be helpful to know if it is a tautology, a contradiction or a contingency. ". A tautology is always true, it never gives you any information about the values of the variables involved. Proposition – The meaning of proposition in literature is an idea, a plan or an offer, or a suggestion that can be proved True or False. Two logical statements are logically equivalent if they always produce the same truth value. Tautology in literal sense refers to different words or a collection of words used to express the same thought or views. Rug tufting is gaining traction as a hobby like never before! If you want to make a tuft rug for yourself or as a gift for your loved ones, you can choose our top-of-the-line monk cloth. The fact that you are "very concerned" about two of the steps indicates to me that you really need to understand why those steps are valid. The expression "raze to the ground" is a tautology, since the word "raze" includes the notion "to the ground". For example, the propositional formula p ∧ q → ¬r could be written as p / q -> ~r , as p and q => not r, or as p && q -> !r . This is a contingency. tautology: 1 n useless repetition “to say that something is `adequate enough' is a tautology ” Type of: repetitiousness , repetitiveness verboseness resulting from excessive repetitions n (logic) a statement that is necessarily true “the statement `he is brave or he is not brave' is a tautology ” Type of: true statement , truth a true statementtautology - WordReference English dictionary, questions, discussion and forums. Proofs are simply the re-expression of statements as other statements without relying on other statements (i. When we speak of propositional logic, we usually speak of the language and the calculus: thus, we say that propositional logic is consistent because we cannot derive ⊥ ⊥ in the. As per the actual tautology definition, there are two forms of explanation for tautology meaning. There were familiarities, parallels, his old address, people he once knew, but people wielded superpowers, wondrous technology and magic beyond his age were used for the most mundane of tasks. When someone says the same thing twice, they’re likely using a tautology. ) This tautology can be corrected by removing one of the repeats. In contrast, consider a statement like: Matt is both 40 years old and not 40 years old. •A valid sentenceor tautologyis one that’s True under all interpretations, no matter what the world is actually like or what the semantics is. It is linked to the following entry on Grammar Monster:12. The symbol commonly used to show two statements are logically equivalent is ⇔ ⇔. If either is true, then the full statement is true. 1 Answer. This. 500 POINTS. Finally, we conclude with future work in. Macauley (Clemson) Lecture 2. All options here are based on order of application of quantifier. [In other words, we. When employed properly, the different literary devices help readers to appreciate, interpret and analyze a literary work. 2 Tautology, in logic, a statement so framed that it cannot be denied without inconsistency. Here (if I understand correctly): Γ Γ is simply a set of sentences. The notation is used to denote. teuthology is an automation framework for Ceph, written in Python. (Here and in the future, I use uppercase letters to represent compound propositions. A place name is tautological if two differently sounding parts of it are synonymous. . Repetition of the same sound is tautophony. After all, if the junction of X X and Y Y does imply Z Z then it shall contradict ¬Z ¬ Z. • Contradiction [ad for cough drop] It’s gone, but it isn’t. I’ve discussed this with colleagues. Each sentence in Example 1 is the disjunction of a statement and its negation Each of these sentences can be written in symbolic form as p~p. For example, the statement "If it rains, then it rains" is a tautology. [Math Processing Error] p → p. In propositional logic and boolean algebra, De Morgan’s laws are a pair of transformation rules that are both valid rules of inference. the use of two words or phrases that express the same meaning, in a way that is unnecessary and usually unintentional: No one talks about " creative music ," because it. Cheryl passes math or Cheryl does not pass math. A tautology is a proposition that is always true, regardless of the truth values of the propositional variables it contains. A measure of a deductive system's power is whether it is powerful enough to prove all true statements. Find step-by-step Calculus solutions and your answer to the following textbook question: Determine whether each argument is valid or invalid. 🔗. This is a tautology. Either way, you can get a hold of high-quality rug tufting. a large amount of something that hangs down: 3. 4 5. b) p → (p ∨ q) c) ¬p → (p → q) d) (p ∧ q) → (p → q)Subject - Discrete MathematicsVideo Name - Tautology, Contradiction and ContingencyChapter - Logic Faculty - Prof. Listen to the audio pronunciation in English. Wasit University. So P = "It is raining" is a poor choice of examples to illustrate the question of the tautology-ness of "P or not-P". Download TUFTOLOGY and enjoy it on your iPhone, iPad, and iPod touch. Essential to the development of all divine name theology is the name YHWH, which, occurs repeatedly throughout the book of Genesis, but is only introduced formally, in direct response to Moses’ request for it, in Exod. It is relatively rare to find tautologies that are rhetorically pleasing. Here is a proof: The first five lines are the same as your proof. Learn more. Visit Stack Exchange16. 00 Tufting Loop pile tufting gun $270. The pieces share a rhythm that is peculiar to DeLillo’s late style, an eerie, circling, self-canceling movement modeled on the tautology, even when it is not itself strictly tautologous. (a) P → P. Two logical formulas p p and q q are logically equivalent, denoted p ≡ q, p ≡ q, (defined in section 2. Tautologies. p ↔ q. This often occurs when a name from one language is imported into another and a standard. An axiom is not a tautology because, to prove that axiom, you must assume at least one axiom: itself. TAKE THE QUIZ TO FIND OUT Origin of tautology 1 First recorded in. Tautology is a literary device whereby writers say the same thing twice, sometimes using different words, to emphasize or drive home a point. ¬ ∃ x ∀ y ( ¬ O ( x) ∨ E ( y)). A tautology is an expression of the same thing twice. p→q. 간단한 예시로 "x가 y와 같거나, x가 y와 같지 않다", "이 공은 녹색이거나 이 공은 녹색이. Tautology: A statement that is always true, and a truth table yields only true results. Savannah Stewart June 14 2021 in Geography. A tautology is a compound statement that will always be true for every value of individual statements. Join our rewards program to earn points, more points you earn more $$ you save! Tuftology Duo 2. Like most proofs, logic proofs usually begin with premises — statements that you’re allowed to assume. by Cole Salao. Show that each of these conditional statements is a tautology by using truth tables. The calculator will try to simplify/minify the given boolean expression, with steps when possible. Tautology - Key Takeaways. Tautology and Logical equivalence Denitions: A compound proposition that is always True is called atautology. Like dual of (p ∧ ¬q) is (p ∨ ¬q) not (¬p ∨ q). Furthermore, it notes that the statement p q p q is automatically true when p p is false, and saying that p q p q is a tautology actually means that q q is true. 800 POINTS. The next tautology K ⊃ (N ⊃ K) has two different letters: “K” and “N”. They have exactly the same meaning. tuftology. 4. Tautology definition. This. Usually, tautology is defined in the context of propositional logic. If an interpretation satisfies a formula, then it does not satisfy the negation of that formula. Definition 2. 0. 2015; D'Angelo and West 2000, p. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket Press Copyright. 3 $egingroup$ If you don't know what a tautology is, you won't really benefit from solving a. Monks cloth is specifically created to be a strong base fabric, perfect for making tufted rugs and punch needling. Express each of these statements using logical operators, predicates, and quantifiers. | Meaning, pronunciation, translations and examplesA tautology is a formula that is "always true" --- that is, it is true for every assignment of truth values to its simple components. You can think of a tautology as a rule of logic. The language is in NP but not in NPC. It’s true when and false when . 0 Cut & Loop tufting gun $249. 2. TAUTOLOGY มีเป้าหมายในการเผยแพร่การศึกษาคุณภาพดีสู่สาธารณชน เพื่อสร้างสังคมแห่งนวัตกรรมtautology. Welcome to Tuftology app! Your one-stop-shop for all things rug tufting! Get ready to unleash your creativity with our top-notch supplies, ranging from vibrant yarns to reliable tufting machines. Applies commutative law, distributive law, dominant (null, annulment) law, identity law, negation law, double negation (involution) law, idempotent law, complement law, absorption law, redundancy law, de. See examples of TAUTOLOGY used in a sentence. p ⇒ q ≡ q¯¯ ⇒ p¯¯¯ and p ⇒ q ≡ p. If you are looking for the best fabric and accessories to make a rug tuft, Tufting. Since the parts of a tautology have identical logical value, the whole will always have the same value of (logical) truth as. Tautology. A triangle is isosceles or a triangle is not isosceles. Then SAT would be in P, and P = NP. The words adequate and enough are two words that convey the same meaning. Let’s look at what makes tautology acceptable or utterly unacceptable. In other words, a contradiction is false for every assignment of truth values. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more. The first method to show that two statements and p and q are equivalent is to build a truth table to to find the truth values of . Create intermediate columns so it is clear how you get the final column, which will show each is a tautology. Theorem (PageIndex{4}): Existence of Prime Factorizations. 1: Compound Statements is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Pamini Thangarajah . $349. Example: It's raining or it's not raining •An inconsistent sentenceor contradictionis a sentence that’s Falseunder all interpretations. — typtologist, n. Example: Prove that the statement (p q) ↔ (∼q ∼p) is a tautology. The phrase, word, or morpheme might be used twice, three times, or more. An example of metonymy is using Wall Street in your writing as a stand-in for the financial sector. Tautological definition: (of a phrase) needlessly repetitive without adding information or clarity. The first two columns will be for the two propositional variables p and q. However. Sorted by: 1. A rhetorical tautology is the redundant restatement of an idea of concept. One stope shop for all your rug tufting supplies. Tautologies tend to be equal parts grammatical and contextual – grammar insists that. This tool generates truth tables for propositional logic formulas. A tautology truth table is a truth table representing a tautology. Udemy Courses Via My Website. " every ", " some ", and "is"), a truth-functional tautology is true because of the logical terms it. • The opposite of a tautology is a contradiction, a formula which is “always false”. Due to its co-NP-completeness, tautology checking aggressively consumes computational power when the size of the problem increases. Suppose ( (P→R)∨ (Q→R)) false. Interpreting Truth Tables. For propositional logic and natural deduction, this means that all tautologies must have natural deduction proofs. tautology meaning: 1. Tufting. 4. If you do all 8 rows, and always get T, then it would show this is a tautology. 9,803 7 39 58. 3. [count] “A beginner who has just started” is a tautology. In other words, a contradiction is false for every assignment of truth values to its simple components. A statement’s being a tautology does not mean that it is provable in certain proof systems. • A compound proposition that is always false is called a contradiction. We use the number 1 to symbolize a tautology. A number is even or a number is not even. Truth tables can be used to sort _ into logically significant _ and to show logically significant _ between statements. I. Tuftology. We then ask what it takes for T -> C to be false. 1 below to verify the logical equivalence and supply a reason for each step? 0 $(P land eg Q) lor P equiv P$ How is this proved using theorems? 0. (As "am" means "in the morning," the phrase "3 am in the morning" is a tautology. Rhetorical and logical tautologies are more interesting. , no circular reasoning). of, relating to, or resembling twilight; dim; indistinct. literary devices refers to the typical structures used by writers in their works to convey his or her messages in a simple manner to the readers. 288). Rhetorical and logical tautologies are more interesting. It is often the case that it is neither raining nor not. In most texts, the assertion that (p(n)) is a tautology would appear as. tuftology (@tuftology) on TikTok | 21 Followers. 2. So from this I suppose I could determine the argument's validity (whether or not I know that is it a tautology) $endgroup$ –This T shows it is not a contradiction. A tautology is any argument where for any combination of truth values (true/false) assigned to the predicates within it, the logical flow of the argument is such that the conclusion will always turn out true. in words other than those of the immediate context, without imparting additional force or clearness, as in “ widow woman”. cascade meaning: 1. So, let’s try to understand the authors’ argument from above. 항진식. Below is a list of literary devices with detailed definition and examples. Mathematical proofs rely on tautologies. – Thesatisfiability problem—decidingifatleastone truth assignment makes the formula true—is NP-complete. In grammatical terms, a tautology is when you use different words to repeat the same idea. You can stop as soon as that happens (and answer "neither"). , if, then, and, or, not, and if and only if. the theory that departed souls communicate with the living by tapping. 🔗. Indeed, intuitionists maintain that it does not apply to mathematics at all, since they hold that. A Greek word is used to derive the tautology where 'tauto' is known as "same" and "logy" is known as logic. The opposite of a tautology is a contradiction, a formula which is "always false". In the PDF textbook, "A Friendly Introduction to Mathematical Logic 2nd Edition" by Christopher C. Proof by Rules A proof is a sequence of assertions, each of which the reader agrees to. A place for people who love tufting, or are just interested in using mechanical guns…To address your actual question, the proof you have given is correct. Solution: Make the truth table of the above statement: p. The word ‘or’ used in this way is called the ‘inclusive or’ and this is the only use of the connective ‘or’ in mathematics. 本当の僕は石原さとみだったらええのになあって--------------------------------vocal：めありー twitter. To construct the table, we put down the letter “T” twice and then the letter “F” twice under the first letter from the left, the letter “K”. That is the meaning of tautology. Soundness Corollary: If T S, then S is a tautology. A tautology gives us no genuine information because it only repeats what we already know. Namely, p and q arelogically equivalentif p $ q is a tautology. tautology in discrete mathematics examplesThen use a truth table to verify each tautology. A tautology consists of a single proposition that supports itself. Not all logical truths are tautologies. 00 In mathematical logic, a tautology (from Greek: ταυτολογία) is a formula or assertion that is true in every possible interpretation. In the instance in question, “It is what it is” counts as spontaneity designed as a communicative cul-de-sac. It helps to use a proof checker to make sure one uses the rules correctly. Recall that. Last column of A in the following sequence - T, T, F, T and last column of B in the following sequence - T, T, F, T. トートロジー（英: tautology, 希: ταυτολογία, 語源はギリシャ語で「同じ」を意味する ταυτο から）とは、ある事柄を述べるのに、同義語 または類語 または同語 を反復させる修辞技法のこと。 同義語反復、類語反復、同語反復等と訳される。関連した概念に冗語があり、しばしば同じ意味. Experience the quality and care of Tuftology®. Definition of tautology noun in Oxford Advanced Learner's Dictionary. Tabel kebenaran adalah sebuah tabel yang memuat semua nilai kebenaran dari kombinasi nilai. When someone says the same thing twice, they’re likely using a tautology. It defies interaction. The left side. Thus, we don’t even have to know what the statement means to know that it is true. If you want a more powerful tufting gun that’s capable of both cut and loop pile, this is the best option (for now). A contradiction is a compound statement that is false for all possible truth values of its variables. Proof by Tautology. Beside distributive and De Morgan’s laws, remember these two equivalences as well; they are very helpful when dealing with implications. “It is what it is” does not invite a response. The compound statement "Either it is raining or it is not raining" is a tautology. Tautology example. 5 License. The characteristic truth table for conjunction, for example, gives the truth conditions for any sentence of the form (A & B). Tautology can be used to add poetic rhythm and beauty to a sentence: “It was the start of the sunset; first the colors muted, then the dusk spread over the forest. com. 10 votes, 19 comments. In rhetoric and logic, a tautology is a statement that is unconditionally true by virtue of its form alone--for example, "You're either lying or. A proposition P is a tautology if it is true under all circumstances. We state it in a form of logical equivalence as follows. Contradiction. 00 Tuftology Tufting gun Boho Daisies $275. One of the company’s co-founders, Omar, was already a huge fan of Tufting and was unhappy with the quality of products available at that time. If a formula P P is a tautology then we can write ∅ ⊨ P ∅ ⊨ P, and it makes sense, since by definition a set of formulas semantically entail another if there does not exist a valuation where all members of the set are true and the other formula is false. Then Join us for an in-person tufting workshop at our Tuftology studio in Springfield VA. The opposite of a tautology is a contradiction or a fallacy, which is "always false". ”.