This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ....
View
Full Document
 Spring '08
 Unkown
 Logic, propositional function, KAIST

Click to edit the document details