Thinking Mathematically Logic 3.6 Negations of Conditional Statements and De Morgan’s Laws

The Negation of a Conditional Statement The negation of p  q is p ^ ~q. This can be expressed as ~(p  q) ≡ p ^ ~q. ~(p  q) and p ^ ~q have opposite truth values for all values of p and q. Exercise Set 3.6 #3 What is the negation of If it is purple, then it is not a carrot.

De Morgans Laws ~(p ^ q) ≡ ~p V ~q

“De Morgans Laws” ~(p V q) ≡ ~p ^ ~q

Examples: DeMorgan’s Laws Exercise Set 3.5 #11, 15 Give an equivalent statement: It is not true that Australia and China are both islands. It is not the case that Jewish scripture gives a clear indication of heaven or an afterlife.

DeMorgan’s Laws Set Theory (A ∩ B)' = A' U B': (A U B)' = A' ∩ B' Logic ~(p ^ q) ≡ ~p V ~q ~(p V q) ≡ ~p ^ ~q

Thinking Mathematically Logic 3.6 Negations of Conditional Statements and De Morgan’s Laws