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VI Implication

VI Implication. 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”. Examples. p: the animal is a beagle

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VI Implication

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  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

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