Two compound statements involving the same components are logically equivalent if they have the same truth tables. For example, the truth table for the statement (¬p) ∨ q is:
By comparing the last column here with the truth table for p ⇒ q (see implication), it can be seen that (¬p) ∨ q and p ⇒ q are logically equivalent. This equivalence is the basis of proof by contradiction.
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