Forms of the Conditional

1. Forms of the Conditional

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

3. 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.

4. 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.

5. 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.

6. Valid conclusion- • Original statement restated (also known as conditional) • contrapositive

7. 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.

8. 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 ______________.