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# dm-lec4-proofs-s - Discrete Mathematics CS204 Lecture#3...

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Unformatted text preview: Discrete Mathematics CS204 Lecture #3 September 9, 2009 at KAIST 1 Some Terminology from the last class Suppose a conditional proposition p → q is true. Then- we may use q as a criterion to test the truth value of p , and- we may use also p as a criterion to test the truth value of q . That is,- If q is false, then p cannot be true. In other words, q needs to be true for p to hold. ◦ q is called a necessary condition for p . 2 Similarly- To show that q is true, it suffices to verify p is true. ◦ p is called a sufficient condition for q . Caution Given a conditional p → q , the converse q → p is not necessarily true. For example, “If I’m rich, I will be happy” does not mean “In order to be happy, I have to become rich”. 3 Quantifiers (Review) Recall- A propositional function P ( x ) associates to each x in the domain of discourse D , a proposition P ( x ) .- The universal quantifier “ ∀ ” makes the propositional function a universally quantified statement ∀ x P ( x ) ◦ which is a proposition that is true if and only if P ( x ) is true for all x ∈ D ....
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dm-lec4-proofs-s - Discrete Mathematics CS204 Lecture#3...

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