Lecture Notes 7 CS1502

1. Lecture Notes 7CS1502 Conditionals

2. Material Conditional • PQP is called the antecedent and Q is called the consequent.

3. Definition of 

5. Q Q P P English Translations • If P then Q • P implies Q • P only if Q • P is sufficient for Q • Q is necessary for P • Q if P

6. English Translation EGsP  Q If P then Q (If you are human then you are a mammal) P implies Q (Being a human implies being a mammal) If P, Q (If you are human, you are a mammal) P only if Q (You’ll live a long time only if you eat veggies) P is sufficient for Q (Knowing you’re living a long time is sufficient to know you eat veggies) Q is necessary for P (Eating veggies is necessary to live a long time) Q if P (You are a mammal if you are human)

7. P  Q Home(max)  Library(claire)Large(b)  Cube(b) If not P then QIf Max is not home, then Claire is at the library If b is not large, then it is a cube Unless P, QUnless Max is at home, Claire is at the library Unless b is large, b is a cube Q, unless P Claire is at the library unless Max is home B is a cube unless b is large Why not  for last two? (section 7.3 and lecture)

8. Equivalences • P  Q • P  Q • Q  P

9. Biconditional • P  Q • Equivalent to (P  Q) ^ (Q  P)

10. English Translations • P if and only if Q • P just in case Q

11. Truth Table for 

12. Equivalencies • P Q • (P  Q)  (Q  P) • (P  Q)  (P  Q) P and Q are sufficient and necessary for each other.

13. Well-formed Formula (wff)(updated definition) • Any atomic sentence is a wff. • If A are B are wffs then so are • A • A  B • A  B • A  B • A  B