Converse, Inverse, Contrapositive
- Given an if-then statement "if p , then q ," we can create three related statements:
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A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause. For instance, “If it rains, then they cancel school.”
- "It rains" is the hypothesis.
- "They cancel school" is the conclusion.
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To form the converse of the conditional statement, interchange the hypothesis and the conclusion.
- The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains."
- To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.
- The inverse of “If it rains, then they cancel school” is “If it does not rain, then they do not cancel school.”
- To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement.
- The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain."
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