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

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

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

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)

Notation ConditionalIf p, then q.Original InverseIf not p, then not q.Negate ConverseIf q, then p.Switch ContrapositiveIf not q, then not p. Switch and Negate

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.

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

examples Example: If a polygon has four sides, then it is a quadrilateral. (true) 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 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) 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) 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) Contrapositive(switch and not): If a polygon is not a quadrilateral, then it does not have four sides. (true)

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.

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