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Is this formula a tautology, a contradiction, or a contingent formula?

(P → Q) ↔ (Q → P)

User Ryggyr
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1 Answer

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The formula (P → Q) ↔ (Q → P) is a tautology.

A tautology is a statement that is always true, regardless of the truth value of the propositions it contains. In this formula, the biconditional statement "if and only if" (↔) connects the two implications "if P, then Q" (P → Q) and "if Q, then P" (Q → P). Because these two implications are logically equivalent, the formula as a whole is always true, regardless of the truth value of P and Q.

A contradiction is a statement that is always false, regardless of the truth value of the propositions it contains.

A contingent formula is a statement that can be either true or false, depending on the truth value of the propositions it contains.

User Dumpen
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