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Related Conditional Statements 2-1B What are the three related conditional statements? How are the three related conditional statements made?

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Presentation on theme: "Related Conditional Statements 2-1B What are the three related conditional statements? How are the three related conditional statements made?"— Presentation transcript:

1 Related Conditional Statements 2-1B What are the three related conditional statements? How are the three related conditional statements made?

2 Related Statements Converse Inverse Contrapositive

3 Converse The converse of a conditional statement is formed by interchanging the hypothesis and the conclusion. (Converse—con—switch)

4 Converse (Switch if-then) Conditional: If you live in Mishawaka, then you live in Indiana. Converse: If you live in Indiana, then you live in Mishawaka.

5 Inverse The inverse of a conditional is formed by taking the negations of the hypothesis and the conclusion. (Negations state the opposite of the original phrase.) Add not or take not out not

6 Inverse (add not) Conditional: If you live in Mishawaka, then you live in Indiana. Inverse: If you don’t live in Mishawaka, then you don’t live in Indiana.

7 Contrapositive The contrapositive of a conditional is formed by taking the negation of the hypothesis and conclusion, then interchanging them. Switch and add not. +not

8 Contrapositive (switch & add not) Conditional: If you live in Mishawaka, then you live in Indiana. Contrapositive: If you don’t live in Indiana, then you don’t live in Mishawaka.

9 If you are a teenager, then you are 15. Converse: If you are 15, then you are a teenager. Inverse: If you are not a teenager, then you are not 15. Contrapositive: If you are not 15, then you are not a teenager. false true false

10 If you water the plants, then the plants will grow. Converse: If the plants grow, then you watered the plants. Inverse: If you don’t water the plants, then the plants will not grow. Contrapositive: If the plants do not grow, then you did not water the plants. true

11 Venn Diagram If you are a surgeon, then you wear a mask. People who wear masks Surgeons A B C

12 Truth Values If a conditional statement is true, its contrapositive is true. If a conditional statement is false, its contrapositive is false. The truth value of a conditional statement does not tell you whether it converse or its inverse it true or false. You must analyze those statements separately.

13 Assignment 2-1B Page 96, 1-8, 10-13

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