1. Inductive and Deductive Reasoning

2. Notecard 30 Definition: Conjecture: an unproven statement that is based on observations or given information.

3. Notecard 31 Definition: Counterexample: a specific case for which a conjecture is false.

4. Counterexample Find a counter example to show that the following conjecture is false. The sum of two numbers is always greater than the larger number.

5. Notecard 32 Definitions: Conditionals, Hypothesis, & Conclusions: A conditional statement is a logical statement that has two parts: If ____ then _____. The hypothesis is the “if” part and it tells you what you are talking about. The conclusion is the “then” part and it describes the hypothesis.

6. Writing a conditional statement Writing the following statements as conditionals. Two angles that make a linear pair are supplementary. All 90 o angles are right angles.

7. Notecard 33 The negation of a statement is the opposite of the original.

8. Negation Negate the following statements. The ball is red. The cat is not black.

9. Notecard 34 Definitions: Inverse, Converse, Contrapositive The converse of a conditional statement switches the hypothesis and conclusion. The inverse of a conditional statement negates both the hypothesis and conclusion The contrapositive of a conditional statement takes the inverse of the converse. (it switches and negates)

10. Writing statements Write the converse, inverse and contrapositive of the conditional statement: “If two angles form a linear pair, then they are supplementary.” Which of these statements are true?

11. Notecard 35 Definition: Biconditional: If a conditional statement and its converse are both true, then we can write it as a biconditional statement by using the phrase if and only if instead of putting it in if-then form. __________ if and only if ___________. (hypothesis) (conclusion)

12. Biconditional Statement Write the following conditional statement as a biconditional statement. If two lines intersect to form a right angle, then they are perpendicular.