Bellringer: Tuesday, September 1 Come up with a conjecture and a counterexample within your groups. Be prepared to share with the class. (you do not have.

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Presentation transcript:

Bellringer: Tuesday, September 1 Come up with a conjecture and a counterexample within your groups. Be prepared to share with the class. (you do not have to write this down)

2.2 Conditional Statements Conditional: an ‘if-then’ statement Ex) If an animal is an eagle, then the animal is a bird. Symbol: p→q (read as ‘if p, then q’) Hypothesis: the part p following if Ex) from previous example, hypothesis: an animal is an eagle. Conclusion: the part q following then Ex) from previous example, conclusion: the animal is a bird.

Example: Conditional: If Auburn does well this year, then Auburn will win the Iron Bowl. Hypothesis (p): Auburn does well this year Conclusion (q): Auburn will win the Iron Bowl

Truth Value: whether the conditional is true or false. Equivalent statements: statements with the same truth value (conditional statements are equivalent to the contrapositive, converse and inverse statements are equivalent) Negation: the opposite of the statement: Ex. Original statement: The sky is blue Negation: The sky is not blue. Ex. Original statement: The grass is not green Negation: The grass is green

StatementHow to write itExampleSymbolsHow to read it ConditionalUse the given hypothesis and conclusion If m ∠ A=15, then ∠ A is acute p→qp→qIf p, then q ConverseExchange the hypothesis and conclusion If ∠ A is acute, then m ∠ A=15 q→pq→pIf q, then p InverseNegate both the hypothesis and conclusion of the conditional If m ∠ A ≠ 15, the ∠ A is not acute. ~p→ ~qIf not p, then not q ContrapositiveNegate both the hypothesis and the conclusion of the converse If ∠ A is not acute, then m ∠ A ≠ 15 ~q→~pIf not q, then not p

Example 1: Conditional (p→q): If you live in Alabama, then you live in the South. Converse (q→p): Inverse (~p→~q): Contrapositive (~q→~p):

Example 2: Conditional (p→q): If an animal is a husky, then the animal is a dog. Converse (q→p): Inverse (~p→~q): Contrapositive (~q→~p):