2.1.2 Conditional Statements (continued)
If given a conditional with hypothesis p and conclusion q , the three related conditionals can be written based on this conditional using the definitions given here. The given conditional’s hypothesis and conclusion are switched to write the converse. The given conditional’s hypothesis and conclusion are both negated, but not switched, to write the inverse. The given conditional’s hypothesis and conclusion are switched and negated to write the contrapositive. In this example, the given conditional statement is “If an animal is a dog, then it has four legs.” Identify the hypotheses and the conclusion of this given conditional and then use the definitions given above to write the conditional’s converse, inverse, and contrapositive. Remember, negating a statement simply means to add “not” to the statement. Notice that the truth value of the conditional and the contrapositive are both true and that the truth value of the converse and inverse are both false. Related conditional statements that have the same truth value are called logically equivalent statements. The Law of Contrapositive states that a conditional and its contrapositive will always be logically equivalent.
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