Conditional Statements

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Presentation transcript:

Conditional Statements Section 2-3

Conditional Statements If-then statements are called conditional statements. The portion of the sentence following if is called the hypothesis. The part following then is called the conclusion. p q (If p, then q)

If it is an apple, then it is a fruit. Hypothesis – It is an apple. Conclusion – It is a fruit. p q

Converse q p The converse statement is formed by switching the hypothesis and conclusion. If it is an apple, then it is a fruit. Converse: If it is a fruit, then it is an apple. The converse may be true or false.

negation – the denial of a statement Ex. “An angle is obtuse.” Negation – “An angle is not obtuse.”

Inverse ~p ~q An inverse statement can be formed by negating both the hypothesis and conclusion. If it is an apple, then it is a fruit. Inverse: If it is not an apple, then it is not a fruit. The inverse may be true or false.

Contrapositive ~q ~p A contrapositive is formed by negating the hypothesis and conclusion of the converse. If it is an apple, then it is a fruit. Contrapositive: If it is not a fruit, then it is not an apple. The contrapositive of a true conditional is true and of a false conditional is false.