Sign In
rc Words: & If¬ q, then ¬ p Symbols: & ¬ q ⇒ ¬ p
Interchanging the hypothesis and the conclusion of the inverse statement can also form the contrapositive of the conditional. Consider the following conditional statement and its related conditionals.
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 |
Inverse | If a figure isnot a square_(¬ p),thenit doesnot have four sides_(¬ q). | ¬ p ⇒ ¬ q |
Contrapositive | If a figure doesnot have four sides_(¬ q),thenit is not a square_(¬ p). | ¬ q ⇒ ¬ p |
The truth table of a contrapositive statement is made using the truth values for its hypothesis ¬ q and conclusion ¬ p.
The contrapositive of a conditional statement has the same truth table as the conditional statement. In other words, a conditional and and its contrapositive are either both true or both false. Therefore, they are equivalent statements.