Give all answers if alb and bla, where a and b are1. Prove or disprove.integers, then a = = b.2. Prove or disprove. if abc, where a,b and c arepositive integers and a 6= 0, then alb or alc.3. Prove or disprove. The product of any two evenintegers is a multiple of 4.4. Prove or disprove. For all integers a,b and c, if alband 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 237. Find a mod m and a div m when (a) a = 9009,m=223 (b) a = -10101,m = 3338. Show that if n is an integer, then n 2 = 0(mod 4)or n 2 = 1( mod 4)

Dear student, these are multiple questions. As per guidelines , I can do only first three question.…

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

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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Give all answers

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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