135_1_-_Solutions

135_1_-_Solutions - Assignment 1 Solutions 1. Is the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
1. Is the statement P = ( Q = R ) equivalent to ( P = Q ) = R ? Give reasons. Solution 1: The statements are not equivalent. To see this let P , Q and R be all false. Then ( Q = R ) and ( P = Q ) are true. Therefore P = ( Q = R ) is true but ( P = Q ) = R is false. Solution 2: P Q R Q = R P = ( Q = R ) T T T T T T T F F F T F T T T T F F T T F T T T T F T F F T F F T T T F F F T T P Q R P = Q ( P = Q ) = R T T T T T T T F T F T F T F T T F F F T F T T T T F T F T F F F T T T F F F T F Since the final columns are not the same, the two statements are not equivalent. In particular, they differ in the bottom row, so the truth value of the statements are different when P , Q and R are all false. 2. Prove that the statements P OR ( Q AND R ) and ( P OR Q ) AND ( P OR R ) have the same truth tables. This is a distributive law . Solution:
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/24/2011 for the course MATH 135 taught by Professor Andrewchilds during the Winter '08 term at Waterloo.

Page1 / 3

135_1_-_Solutions - Assignment 1 Solutions 1. Is the...

This preview shows document pages 1 - 2. Sign up to view the full document.

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