1. VI Implication

2. Definition • Let p and q be any two statements, p implies q if and only if p v q Ξ q • aka p implies q if the statement “p or q” is logically equivalent to the statement q • p q is read “p implies q” • p q is read “p does not imply q”

3. Examples • p: the animal is a beagle • q: the animal is a dog • We can say p q bc The animal is a beagle or the animal is a dog is logically equivalent to The animal is a dog

4. Prove this relationship [(p  q) ^ ~q ] ~ p To prove this we need to show [(p  q) ^ ~q ] v ~ p Ξ ~ p WHY????? p implies q if and only if p v q Ξ q

5. Lets look it another way

6. SO LETS PROVE IT [(p  q) ^ ~q ] v ~ p Ξ ~ p

7. Prove another [(p  ~q) ^ q ] q

8. HOMEWORK 5 Use a truth table to prove [ (p  q) ^ p ] q