homework1

homework1 - R P R ∨ Q R b Verify that P ∨ Q ...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
HOMEWORK 1. DUE FRIDAY, 4/1. SERIOUSLY. MATH 131A, SPRING 2011, STOVALL To turn in: Problem 1: Let P and Q be mathematical statements. Use truth tables to verify that a) ( P Q ) ( P ) ( Q ) b) ( P Q ) ( P ) ( Q ) c) ( P = Q ) P ( Q ) Problem 2: Simply the following negations: a) [( P = Q ) = ( S = U )] b) [ P 1 and for every n N , P n = P n +1 ] c) [For every natural number n , there exists a natural number m such that P ( n,m )] (Here P ( n,m ) is a statement that depends on n and m , e.g. “ n is prime and m n ”.) Problem 3: Let A,B , and C be sets. Show that A \ ( B C ) = ( A \ B ) ( A \ C ). Recommended: Let P,Q,R be mathematical statements. a) Verify that ( P Q )
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: R ≡ ( P ∧ R ) ∨ ( Q ∧ R ). b) Verify that P ∨ ( Q ∧ R ) ≡ ( P ∨ Q ) ∧ ( P ∨ R ). c) Give three specific, concrete mathematical statements P,Q,R such that P ∨ ( Q ∧ R ) is true but ( P ∨ Q ) ∧ R is false. Simplify the following negations: a) ∼ [ ∀ n ∈ N , P n ∨ Q n ] b) ∼ [For some n ∈ N , P ( n,m ) holds for every m ∈ N ] Let A,B,C be sets. Prove that a) A ∩ ( B \ C ) = ( A ∩ B ) \ ( A ∩ C ) . b) ( A \ B ) ∪ B = A if and only if B ⊆ A . 1...
View Full Document

This note was uploaded on 09/23/2011 for the course MATH 131 taught by Professor Eskin during the Spring '10 term at UCLA.

Ask a homework question - tutors are online