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The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
In mathematics, theorems are often stated in the form "P is true if and only if Q is true". Because, as explained in previous section, necessity of one for the other is equivalent to sufficiency of the other for the first one, e.g. P ⇐ Q {\displaystyle P\Leftarrow Q} is equivalent to Q ⇒ P {\displaystyle Q\Rightarrow P} , if P is necessary ...
Logical consequence is necessary and formal, by way of examples that explain with formal proof and models of interpretation. [1] A sentence is said to be a logical consequence of a set of sentences, for a given language , if and only if , using only logic (i.e., without regard to any personal interpretations of the sentences) the sentence must ...
Conditional sentences can take numerous forms. The consequent can precede the "if"-clause and the word "if" itself may be omitted or replaced with a different complementizer. The consequent can be a declarative, an interrogative, or an imperative. Special tense morphology can be used to form a counterfactual conditional. Some linguists have ...
An argument is formally valid if and only if the denial of the conclusion is incompatible with accepting all the premises. In formal logic, the validity of an argument depends not on the actual truth or falsity of its premises and conclusion, but on whether the argument has a valid logical form.
A aggravate – Some have argued that this word should not be used in the sense of "to annoy" or "to oppress", but only to mean "to make worse". According to AHDI, the use of "aggravate" as "annoy" occurs in English as far back as the 17th century. In Latin, from which the word was borrowed, both meanings were used. Sixty-eight percent of AHD4's usage panel approves of its use in "It's the ...
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
/ "Inflammable" can only mean "not flammable." The word "inflammable" can be derived by two different constructions, both following standard rules of English grammar: appending the suffix -able to the word inflame creates a word meaning "able to be inflamed", while adding the prefix in-to the word flammable creates a word meaning "not flammable".
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