WARM UP Get Ready To Be Logical!

1. WARM UPGet Ready To Be Logical! • 1. Books and notebooks out. • 2. Supplies ready to go. • 3. Answer the following: The sum of 2 positive integers is ___________ True or False For all integers n, is positive. 2 complementary angles cannot be .

2. Logic Inductive Reasoning is a process of reasoning that a rule or statement is true because of a specific case that is usually drawn from a pattern or observation. Examples Conjecture 1, 2, 4, 7, 11, _____ Jan, March, May, ______

3. Deductive Reasoning is a process of using logic to draw conclusions using definitions, facts, or properties. This may include postulates and theorems.

4. Conditional If p, then q. p is hypothesisq is conclusion p→q If I work hard, then I will succeed. Converse If q, then p. Flip q→p If I will succeed, thenI worked hard.

5. Conditional If p, then q. p→q If I work hard, then I will succeed. Inverse If not p, then not q negate ~p→~q If I don’t work hard, then I will not succeed. Contrapositive If not q, then not p flip & negate ~q→~p If I don’t succeed, then I didn’t work hard.

6. True or False That is the Question??? To prove a statement false, one must provide a counterexample. A counterexample is a drawing, statement or number. The counterexample must satisfy the hypothesis but fail to satisfy the conclusion. • Look for a pattern • Make a conjecture • Prove or find a counterexample

7. Prove or find a counterexample For all integers n, is positive. 2 complementary angles cannot be .

8. Truth value-- is true in all situations except when hypothesis is true and the conclusion is false. p = you make an A q = I will buy you a car p q p → q T TYou made an A, then I bought the car. T T FYou made an A, but I did not buy the car. F F TYou did not make an A, but I bought the car anyway. T F FYou did not make an A, then I did not buy the car. T

9. Write the converse, inverse, and contrapositive of the following. State if true or false. If false give counterexample. If m<A = 30, then <A is acute.

10. If m<A = 30, then <A is acute. p → q Converse q → p If <A is acute, then m<A = 30. Inverse ~p → ~q If m<A ≠30, then <A is not acute. Contrapositive ~q → ~p If <A is not acute, then m<A ≠ 30.

11. Write the converse, inverse, and contrapositive of the following. State if true or false. If false give counterexample. If 2 angles are vertical, then they are

12. If 2 angles are vertical, then they are p → q Converse q → p If 2 angles are , then they are vertical. Inverse ~p → ~q If 2 angles are not vertical, then they are not Contrapositive ~q → ~p If 2 angles are not , then they are not vertical.

13. HW: p.77 # 8-14 even 18-22 even 24-27 allp. 85 14-20 even, 24-29 all