a,b,c,d are nonnegative integers. be the proposition that d is even, let W be the proposition that exactly one among a, b,c en, and let T be the proposition that all three are even. by cases that

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Proofs in Overleaf

(a) Suppose that
a +b+c = d,
where a, b,c,d are nonnegative integers.
Let P be the proposition that d is even, let W be the proposition that exactly one among a, b, c
are even, and let T be the proposition that all three are even.
Prove by cases that
P = [W v T].
(b) Now, suppose that
+x² +y° :
= ?,
w +x +,
%3D
where w,x, y, z are nonnegative integers. Let P be the proposition that z is even, and let R be
the proposition that all three of w, x, y are even.
Prove by cases that
P = R.
Transcribed Image Text:(a) Suppose that a +b+c = d, where a, b,c,d are nonnegative integers. Let P be the proposition that d is even, let W be the proposition that exactly one among a, b, c are even, and let T be the proposition that all three are even. Prove by cases that P = [W v T]. (b) Now, suppose that +x² +y° : = ?, w +x +, %3D where w,x, y, z are nonnegative integers. Let P be the proposition that z is even, and let R be the proposition that all three of w, x, y are even. Prove by cases that P = R.
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