For each of the statements below, determine for yourself if the statement is true or false. If it is true, write a direct proof. If it is false, use a counterexample to show that it is false (a) For all integers m and n, if mn ≡ 0 (mod 8), then m ≡ 0 (mod 8) or n ≡ 0 (mod 8). (b) For all integers a, if a ≡ 7 (mod 10), then a^2 ≡ 9 (mod 10).
For each of the statements below, determine for yourself if the statement is true or false. If it is true, write a direct proof. If it is false, use a counterexample to show that it is false (a) For all integers m and n, if mn ≡ 0 (mod 8), then m ≡ 0 (mod 8) or n ≡ 0 (mod 8). (b) For all integers a, if a ≡ 7 (mod 10), then a^2 ≡ 9 (mod 10).
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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For each of the statements below, determine for yourself if the statement is true or
false. If it is true, write a direct proof. If it is false, use a counterexample to show that it is false
(a) For all integers m and n, if mn ≡ 0 (mod 8), then m ≡ 0 (mod 8) or
n ≡ 0 (mod 8).
(b) For all integers a, if a ≡ 7 (mod 10), then a^2 ≡ 9 (mod 10).
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