MM1G2.b.

1. Destiny and Scott MM1G2.b. Understand and use the relationships among the statement and it converse inverse and contrapositive.

2. Statement • Statement: a sentence that is either true or false, but not both • Example that is a statement: • A triangle has three sides. • Example that is not a statement: • Close the door

3. Conditional statement • Conditional Statement: a logical statement with two parts usually in “if-then” form • It has two parts: the hypothesis (“if” part) and the conclusion (“then” part)

4. Notation

5. True or false For a conditional statement to be true, that means that whenever the hypothesis is true, the conclusion is true also, with no exceptions! So, if there is even ONE exception, then you say it’s false! If you can come up with an exception that would be called a counterexample.

6. **A good way to remember that converse means to switch is to think about “converse” shoes switching back and forth when you are walking.

7. examples • Example: If a polygon has four sides, then it is a quadrilateral. (true) • What is the hypothesis? A polygon has four sides What is the conclusion? It is a quadrilateral • Inverse(not): If a polygon does not have four sides, then it is not a quadrilateral. (true) • Converse(switch): If a polygon is a quadrilateral, then it has four sides. (true) • Contrapositive(switch and not): If a polygon is not a quadrilateral, then it does not have four sides. (true)

8. contrapositive • ***The contrapositive is always logically equivalent to the original statement. • Meaning that if the conditional statement is true, the contrapositive must also be true.

9. Our examples! How do you tell if its contrapositive? What does converse do? What does inverse do? Switches It has not in it (negates) Its switches and negates. Click on questions to get answers