1. Section 2.4 Conditional Statements

2. The word “logic” comes from the Greek word logikos, which means “reasoning.” • We will be studying one basic type of logic statement: a conditional statement or if – then statement • EX: If you study at least 3 hours, thenyou will pass the test.

3. Conditional statement or if-thenstatement • 2 parts • Hypothesis(given) if • Conclusion(prove) after comma or then • “If p then q” or p  q • Theconverseof the conditional statement is formed by interchanging the hypothesis and conclusion. The converse of p  q is q  p.

4. To prove a conditional and/or its converse is true, it MUST be true for all cases. To prove it false, only one example is needed(counterexample). • In a counterexample the hypothesis is fulfilled, but the conclusion is not. • Ex: If an animal is a panther, then it is a cat (T) • Hypothesisconclusion • Ex: If an animal is a cat, then it is a panther (F) • Hypothesis conclusion (lion)

5. Biconditional statement: • A single statement that is equivalent to writing the conditional statement AND its converse. • “p if and only if q,” is written as p q. • Example :An angle is a right angle if and only if it measures 90o.

6. EXS: • Conditional: • If 2 lines are perpendicular, then they form right angles • Converse: • If 2 lines form right angles, then the lines are perpendicular. • Biconditional: • Two lines are perpendicular if and only if the lines form a right angle.

7. Original Statementp q “if p, then q • Converse of the Originalq  p “if q, then p • Biconditionalp  q “p if and only if q”

8. Translate into conditional statements: • 1. The defendant was in Dallas only on Saturday • 2. Court begins only if it is 10 am.

9. Postulates Cont. • Postulate 5: Through any 2 distinct points there exists exactly one line. • Postulate 6: A line contains at least 2 points • Postulate7: Through any three noncollinear points there exists exactly one plane.

10. Postulate 8: A plane contains at least three noncollinear points • Postulate 9: If two distinct points lie in a plane, then the line containing them lies in the plane • Postulate 10: If two distinct planes intersect, then their intersection is a line.