Logic

1. Logic Inductive Reasoning – a process of reasoning that a rule or statement is true because of a specific case (drawn from a pattern) Look for a pattern Make a conjecture Prove or find a counterexample To disprove need a counterexample (a drawing, statement or number)

2. Deductive Reasoning – Process of using logic to draw conclusions using definitions, facts, or properties. ( postulates and Theorems are facts) Examples Conjecture • 1, 2, 4, 7, 11, _____ • Jan, March, May, ______

3. Complete- The sum of 2 positive integers is ___________ Prove or find a counterexample For all integers n, is positive. 2 complementary angles can not be

4. Conditional If p, then q p is hypothesisq is conclusion p→q Converse If q, then p flip q→p Inverse If not p, then not q negate ~p→~q Contrapositive If not q, then not p flip & negate ~q→~p

5. Truth value is true in all situations except when hypothesis is true and the conclusion is false. p = If you make an A q = I will buy you a car p → q T TTYou made an A, then I bought the car. T FFYou made an A, but I did not buy the car. F TTYou did not make an A, but I bought the car anyway. F T F You did not make an A, then I did not buy the car. Counterexample : Make the if true and the then false.

6. 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.

7. 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.

8. 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

9. 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.

10. Biconditional p if and only if q p↔q All definitions are biconditional. Two angles are supplementary if and only if their sum is 180°.