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tautologically

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tautologically
tautologically, adv. (tɔːtəʊˈlɒdʒɪkəlɪ) [f. prec. + -ly2.] In a tautological manner, with tautology.1620 T. Granger Div. Logike 292 Handle the same matter (homogeneously, not tautologically). 1820 Coleridge Let. C. A. Tulk 17 July in Pearson's Catal. (1894) 14 At once superfluous and defective, taut... Oxford English Dictionary
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STIRT
The acronym STIRT is sometimes tautologically, and hence incorrectly, followed by the term trading (as in 'STIRT trading'). Derivatives (finance) wikipedia.org
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Tautological implication Determine whether or not $((P\land Q)\implies R)$ tautologically implies $((P\implies R)\lor (Q\implies R))$ How do I determine that $((P\land Q)\implies R)$ tautologically implies $((P\impli...
A formula A either will tautologically imply another formula B, or it will not do so. So, it is not the case that A does not tautologically imply B.
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Tautological consequence
It follows from the definition that if a proposition p is a contradiction then p tautologically implies every proposition, because there is no truth valuation Similarly, if p is a tautology then p is tautologically implied by every proposition. wikipedia.org
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Show that α is tautologically equivalent to β iff (α↔β) is a tautology? α|==|β iff |= (α↔β) Does anyone know how to go about showing that this is true?
**HINT:** First, assume that $\alpha\leftrightarrow\beta$ is a tautology. Suppose that $g$ is some assignment of truth values to the relevant propositional variables. Since $\alpha\leftrightarrow\beta$ is true in this assignment, conclude that if $\alpha$ was true then $\beta$ is true, and vice vers...
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Ardskenish
History The name "Ardskenish" may mean "Skiði's headland", being Norse and "àird" being added tautologically from Gaelic. wikipedia.org
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How can a set tautologically imply every wff? Let Σ be a subset of Wp such that for some wff a, Σ |= a and Σ |= ¬a. How do I prove that Σ |= b for all b in Wp? I understand that a and ¬a will be satisfied when Σ is ...
From comments by user Mauro ALLEGRANZA: > If $\Sigma \models A$ and $\Sigma \models \neg A$, this means that there is **no** valuation that satisfy $\Sigma$. > > Apply this to show $\Sigma \models B$ by contradiction.
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Ifín
primary forfeda as vowels, [p] had again to be expressed as a modification of [b], called Peithe, after Beithe, also called beithe bog "soft beithe" or, tautologically wikipedia.org
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Tautological Implication of Conditional Statements Does $P \Rightarrow Q $ and $Q \Rightarrow R$ tautologically imply $(P \land Q)\Rightarrow(Q\land R)$ and $(P\lor Q)\Rightarrow(Q\lor R) $? \begin{array}{llr} 1\. & ...
Yes. Just informally: For the first one: if $P \land Q$, then $Q$, and thus (given $Q \rightarrow R$) you get $R$. So you have $Q$ and $R$, and so $Q \land R$ For the second: if $P \lor Q$, then either $P$ or $Q$ (or both). If $Q$, then certainly $Q \lor R$, and if $P$, then (given $P \rightarrow Q$...
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Brynsadler
Amenities The A4222 main road to Cowbridge runs through the village; locally it is known tautologically as 'Brynsadler hill'. wikipedia.org
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Proof there was no tautologically equivalent wff to $(A\leftrightarrow B)$, constructed only by conditional symbol . The way I did was to simply construct a truth table about $\rightarrow$, and treat the 2,3 line as o...
Consider any expression using only the implication $\to$. Possibly it is very long, such as $(((A\to B)\to ((A\to A)\to(B\to A)))\to (A\to B))$ or what have you. Perhaps it has millions of symbols, or just a few. In any case, consider the very last propositional variable that appears in the statemen...
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Qiong Lake
Qiong Lake (), sometimes tautologically referred to as Qionghai Lake, is a freshwater lake in Liangshan Prefecture, Sichuan, and is the second largest wikipedia.org
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What's the proper way to prove P$\rightarrow$Q is not tautologically equivalent to Q$\rightarrow$P I want to rigorously show that [$(p \rightarrow q)\equiv(q \rightarrow q)$] is not true. $Let A =(p \rightarrow q), B...
The most straightforward way is to construct the truth tables and see that they are not equal. Or you could show values of $P$ and $Q$ that make them different (which would amount to mention the specific line of the truth tables where they differ). If $P$ is true and $Q$ is false, then $P\to Q$ is f...
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Longmen Mountains
The Longmen Mountains (), also tautologically referred to in English-language publications as the Longmenshan Mountains, are a mountain range in Sichuan wikipedia.org
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Conjunction of Clauses and Well-Formed Formulas Here is a theorem in my notes: > If $\phi$ is any wff such that $\neg \phi$ is not a tautology, then $\phi$ is tautologically equivalent to a conjunction of clauses. M...
._ The statement: > If $\varphi$ is any wff such that $\varphi$ is not a tautology, then $\lnot \varphi$ is tautologically equivalent to a conjunction According to the theorem stated in your question (applied to $\lnot \varphi$), $\lnot \varphi$ is tautologically equivalent to a conjunction of clauses
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