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The inverse of a conditional statement is a statement that negates the hypothesis p and the conclusion q of the conditional. An inverse statement can be written in if-then form.
rcc & Conditional & Inverse [0.5em] [-0.5em] Words: & Ifp, then q & If notp, then not q Symbols: & p ⇒ q & ¬ p ⇒ ¬ q
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 |
| Inverse | If a figure is not a square_(¬ p),thenit does not have four sides_(¬ q). | ¬ p ⇒ ¬ q |
By considering the truth table for a conditional statement, the conditions under which its inverse is true can be determined.
The inverse of a conditional statement is false only when, in the original statement, the hypothesis is false and the conclusion is true. In any other case, the inverse of a conditional statement is 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.