1. Lesson Aim: How do we recognize converses, inverses, contrapositive & conditional statements? Lesson Objectives: SWBAT Recognize converses, inverses, contrapositive & conditional statements

2. Do Now: State whether these statements are true.  If you get 65% on the regents then you will receive a passing grade.  If it is raining then it must be sunny.  If earth is a star then the sun is a planet.  If a whale is a mammal then the clownfish is a mammal.

3. Response to DO NOW  If you get 65% on the regents then you will receive a passing grade. TRUE  If it is raining then it must be sunny. FALSE  If earth is a star then the sun is a planet. TRUE  If a whale is a mammal then the clownfish is a mammal FALSE Red –True Blue-False

4. CONDITIONAL STATEMENTCONDITIONAL STATEMENT  A conditional is a compound statement formed by combining two sentences (or facts) using the words "if... then.".  The part following the if… is the hypothesis and the part following then is the conclusion.

5. EXAMPLE  If a polygon has three sides, then it is a triangle.

6. TRUTH TABLE FOR CONDITIONAL

7. CONVERSE STATEMENTCONVERSE STATEMENT  The converse of a conditional statement is formed by interchanging the hypothesis and conclusion of the original statement. In other words, the parts of the sentence change places. The words "if" and "then" do not move.

8. EXAMPLE  If it is a triangle, then a polygon has three sides.

9. TRUTH TABLE FOR CONVERSE

10. INVERSE STATEMENTINVERSE STATEMENT  The inverse of a conditional statement is formed by negating the hypothesis and negating the conclusion of the original statement. In other words, the word "not" is added to both parts of the sentence.

11. EXAMPLE OF INVERSE STATEMENT  If a polygon does NOT have three sides, then it is NOT a triangle.

12. TRUTH TABLE FOR INVERSE STATEMENT

13. CONTRAPOSITIVE STATEMENT  The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then interchanging the resulting negations. In other words, the contrapositive negates and switches the parts of the sentence. It does BOTH the jobs of the INVERSE and the CONVERSE. 

14. EXAMPLE FOR CONTRAPOSITIVE If it is NOT a triangle then a polygon does NOT have three sides.

15. TRUTH TABLE FOR CONTRAPOSITIVE

16. QUESTION  Look at the truth table for the Conditional and the Contrapositive, what do you notice?   Look at the truth tables for Converse and Inverse. 

17. LOGICALLY EQUIVALENT  WHEN STATEMENT HAVE THE SAME LOGIC & TRUTH VALUE, THEY ARE SAID TO BE LOGICALLY EQUIVALENT.

18. Independent Work Period  : 20 minutes

19. Closure Let’s examine the following, identify the type of statement as conditional, converse, inverse, or contrapositive and its truth value. If I am sleeping, then I am breathing. If I am breathing, then I am sleeping. If I am not sleeping, then I am not breathing. If I am not breathing, then I am not sleeping.