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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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

This note was uploaded on 02/04/2010 for the course COMPUTER S Cs206 taught by Professor Unkown during the Spring '08 term at Korea Advanced Institute of Science and Technology.

Page1 / 14

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online