Forms of the Conditional. Conditional- Implication. Original statement in if… then… form. p→q If you see a black widow, then you see a spider.

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Presentation transcript:

Forms of the Conditional

Conditional- Implication. Original statement in if… then… form. p→q If you see a black widow, then you see a spider.

Converse- Implication formed by interchanging the hypothesis p and the conclusion q. q→p If you see a spider, then you see a black widow.

Inverse- Implication formed from negating each statement of p→q. ∼ p→ ∼ q If you do not see a black widow, then you do not see a spider.

Contrapositive- Implication formed by negating the statement of the converse. ∼ q→ ∼ p If you do not see a spider, then you do not see a black widow.

Valid conclusion-  Original statement restated (also known as conditional)  contrapositive

Conditional: If you see a black widow, then you see a spider. Converse: If you see a spider, then you see a black widow. Inverse: If you do not see a black widow, then you do not see a spider. Contrapositive: If you do not see a spider, then you do not see a black widow.

Practice! 1. All cows eat grass. Bessie is a cow, therefore ____________. 2. All surfers like big waves. Joe does not like big waves, therefore ______________. 3. All girls attend Meredith College. Dana attends Meredith College, therefore _____________. 4. All redheads have freckles. Mrs. Harrell is not a redhead, therefore ______________.