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The converse of a conditional statement is a statement that exchanges the hypothesis p and the conclusion q of the conditional. A converse statement can be written in if-then form.
rcc & Conditional & Converse [0.5em] [-0.5em] Words: & Ifp, then q & Ifq, then p Symbols: & p ⇒ q & q ⇒ p
This can be better understood with an example.
| Example | Symbols | |
|---|---|---|
| Conditional | If a figure is a square_p,thenit has four sides_q. | p ⇒ q |
| Converse | If a figure has four sides_q,thenit is a square_p. | q ⇒ p |
By considering the truth table for a conditional statement, the conditions under which its converse is true can be determined.
The converse of a conditional statement is false only when the hypothesis is false and the conclusion true. In any other case, the converse of a conditional statement is always true. The explanation for each row of the truth table is similar to the explanation for each row of the truth table for conditional statements.