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Forms of the Conditional

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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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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.

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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.

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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.

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

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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.

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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 ______________.

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2.2 Conditional Statements and 2.3 Using deductive Reasoning to Verify Conjectures.

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