Lecture Notes 7 CS 1502 Conditionals 1 Material

Lecture Notes 7 CS 1502 Conditionals 1

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

Definition of 3

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

English Translation EGs P 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) 6

P Q Home(max) Library(claire) Large(b) Cube(b) If not P then Q If Max is not home, then Claire is at the library If b is not large, then it is a cube Unless P, Q Unless 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) 7

Equivalences P Q P Q Q P 8

Biconditional P Q Equivalent to (P Q) ^ (Q P) 9

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

Truth Table for 11

Equivalencies P Q (P Q) (Q P) (P Q) ( P Q) P and Q are sufficient and necessary for each other. 12

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 13