Conditional & B iconditional

1. Conditional & Biconditional Chapter 3 section 3

2. Conditional • The p is called the hypothesis and the q is called the conclusion.

3. Examples • I am an owner of a small factory, a rush order must be filled out by Monday. I approach you with this generous offer: • p = You work for me on Saturday. • q = I’ll give you a $100 bonus. • If you work for me on Sat., then I’ll will give you a $100 bonus.

4. Case 1 • You come to work and you receive the bonus. • If p is true and q is true. • Case 2 • You come to work and you don’t receive the bonus. • If p is true then q is false.

5. Case 3 • You don’t come to work, but I will give you a bonus. • If p is false, then q is true. • Case 4 • You don’t come to work and you don’t receive the bonus. • If p is false, then q is false.

6. Case 3 explaination • Do you understand why? • In mathematics we tend to use if…then statements a little different. Do not read more into my statement. You do not expect to get the bonus if you did not come to work because that is your experience. I never said that. You are assuming this condition.

8. Biconditional • Iff- if and only if. • It means that two statements say the same thing.

9. Examples • x+3 = 7 iff x = 4 • Today is Monday iff tomorrow is Tuesday.

10. Table