LogicInductive Reasoning – a process of reasoning that a rule or statement is true because of a specific case (drawn from a pattern)1. Look for a pattern2. Make a conjecture3. Prove or find a counterexample

To disprove need a counterexample (a drawing, statement or number)

• Deductive Reasoning – Process of using logic to draw conclusions using definitions, facts, or properties. ( postulates and Theorems are facts)

Examples Conjecture1. 1, 2, 4, 7, 11, _____

2. Jan, March, May, ______

• Complete- The sum of 2 positive integers is ___________

Prove or find a counterexampleFor all integers n, is positive.

2 complementary angles can not be

3n

Conditional If p, then q p is hypothesis q is conclusion

p→q

Converse If q, then p flip

q→pInverse If not p, then not q negate

~p→~qContrapositive If not q, then not p flip & negate

~q→~p

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 T T You made an A, then I bought the car.

T F F You made an A, but I did not buy the car.

F T T You 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.

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.

If m<A = 30, then <A is acute. p → q

Converse q → p If <A is acute, then m<A = 30.

Inverse ~p → ~qIf m<A ≠30, then <A is not acute.

Contrapositive ~q → ~pIf <A is not acute, then m<A ≠ 30.

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

If 2 angles are vertical, then they are p → q

Converse q → p If 2 angles are , then they are vertical.

Inverse ~p → ~qIf 2 angles are not vertical, then they are not

Contrapositive ~q → ~pIf 2 angles are not , then they are not vertical.

Biconditional

p if and only if qp↔q

All definitions are biconditional.Two angles are supplementary if and only if their

sum is 180°.