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1. Prove or disprove. integers, then a = b. if alb and bla, where a and b are 2. Prove or disprove. if albc, where a,b and care positive integers and a 6= 0, then a/b or alc. 3. Prove or disprove. The product of any two even integers is a multiple of 4.

1. Prove or disprove. integers, then a = b. if alb and bla, where a and b are 2. Prove or disprove. if albc, where a,b and care positive integers and a 6= 0, then a/b or alc. 3. Prove or disprove. The product of any two even integers is a multiple of 4.

Database System Concepts
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
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if alb and bla, where a and b are 1. Prove or disprove. integers, then a = = b. 2. Prove or disprove. if abc, where a,b and c are positive integers and a 6= 0, then alb or alc. 3. Prove or disprove. The product of any two even integers is a multiple of 4. 4. Prove or disprove. For all integers a,b and c, if alb and alc, then a|(2b-3c) 5. Suppose that a and b are integers, a = 4( mod 13), and b = 9( mod 13). Find the integer c with 0≤c≤ 12 such that c = 9( mod 13). 6. Evaluate 155 mod 19 and -221 mod 23 7. Find a mod m and a div m when (a) a = 9009,m= 223 (b) a = -10101,m = 333 8. Show that if n is an integer, then n 2 = 0(mod 4) or n 2 = 1( mod 4)
Transcribed Image Text:if alb and bla, where a and b are 1. Prove or disprove. integers, then a = = b. 2. Prove or disprove. if abc, where a,b and c are positive integers and a 6= 0, then alb or alc. 3. Prove or disprove. The product of any two even integers is a multiple of 4. 4. Prove or disprove. For all integers a,b and c, if alb and alc, then a|(2b-3c) 5. Suppose that a and b are integers, a = 4( mod 13), and b = 9( mod 13). Find the integer c with 0≤c≤ 12 such that c = 9( mod 13). 6. Evaluate 155 mod 19 and -221 mod 23 7. Find a mod m and a div m when (a) a = 9009,m= 223 (b) a = -10101,m = 333 8. Show that if n is an integer, then n 2 = 0(mod 4) or n 2 = 1( mod 4)
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