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Wednesday, October 24 th Aim: In what other ways can we potentially change the truth value of a conditional statement? Do Now: Write a TRUE conditional.

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Presentation on theme: "Wednesday, October 24 th Aim: In what other ways can we potentially change the truth value of a conditional statement? Do Now: Write a TRUE conditional."— Presentation transcript:

1 Wednesday, October 24 th Aim: In what other ways can we potentially change the truth value of a conditional statement? Do Now: Write a TRUE conditional statement, and its inverse.

2 Converse Statements To make the converse of a conditional statement, switch the order of the hypothesis and the conclusion: If a quadrilateral is a square, then it has 4 right angles. If a quadrilateral has 4 right angles, then it is a square.

3 Converse If it is sunny, then I will go swimming. If I go swimming, then it is sunny. If it is Sunday, then I do not go to school. If I do not go to school, then it is Sunday.

4 Contrapositive Statements The contrapositive of a conditional statement is the combination of the inverse and the converse: SWITCH and NEGATE If it is raining, then I carry an umbrella. If I do not carry an umbrella, then it is not raining. The contrapositive ALWAYS has the same truth value as the original statement!!! “Logically Equivalent”

5 Contrapositive If a person is eligible to vote, then that person is a citizen. If a person is not a citizen, then that person is not eligible to vote. If I am tall, then I will bump my head. If I do not bump my head, then I am not tall. If I did not eat, then I am hungry. If I am not hungry, then I did eat.

6 Practice with All Four Given the conditional statement: If Julie has money, then she buys a car. Inverse: Converse: Contrapositive:

7 Practice with All Four Given the conditional statement: If a polygon has 3 sides, then it is a triangle. Inverse: Converse: Contrapositive:

8 True Statement & True Converse? If BOTH the original statement AND the converse are true, you can write the BICONDITIONAL statement: If a polygon has 3 sides, then it is a triangle. C: If a polygon is a triangle, then it has 3 sides. Biconditional: A polygon is a triangle IF AND ONLY IF it has 3 sides.

9 Can We Write the BiConditional? Statement: If the sun rises in the east, then it sets in the west. Converse: If the sun sets in the west, then it rises in the east. BiConditional?: The sun rises in the east if and only if it sets in the west!

10 Review Conditional Statement: IF-THEN Inverse: NEGATE hypothesis & conclusion Converse: SWITCH hypothesis & conclusion Contrapositive: NEGATE and SWITCH

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