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, then you will pass the test.

3. Conditional statement or if-then statement 2 parts Hypothesis(given) if Conclusion(prove) after comma or then “If p then q” or p  q The converse of 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) Hypothesisconclusion(lion)

5. Biconditional statement: If a conditional and its converse are both true it can be combined into single statement using words “if and only if” 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 90 o.

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 Statement p  q “if p, then q Converse of the Original q  p “if q, then p Biconditional p  q “p if and only if q”

8. Translate into conditional statements: 1. The defendant was in Dallas only on Saturday If the defendant was in Dallas then it was a Saturday

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.