44. Which of these collections of subsets are partitions of the set of integers? a) the set of even integers and the set of odd integers b) the set of positive integers and the set of negative in- tegers c) the set of integers divisible by 3, the set of integers leaving a remainder of 1 when divided by 3, and the set of integers leaving a remainder of 2 when divided by 3

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 10E: 10. Prove or disprove that the set of all nonzero integers is closed with respect to a. addition...
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44. Which of these collections of subsets are partitions of the
set of integers?
a) the set of even integers and the set of odd integers
b) the set of positive integers and the set of negative in-
tegers
c) the set of integers divisible by 3, the set of integers
leaving a remainder of 1 when divided by 3, and the
set of integers leaving a remainder of 2 when divided
by 3
d) the set of integers less than – 100, the set of integers
with absolute value not exceeding 100, and the set of
integers greater than 100
e) the set of integers not divisible by 3, the set of even
integers, and the set of integers that leave a remainder
of 3 when divided by 6
Transcribed Image Text:44. Which of these collections of subsets are partitions of the set of integers? a) the set of even integers and the set of odd integers b) the set of positive integers and the set of negative in- tegers c) the set of integers divisible by 3, the set of integers leaving a remainder of 1 when divided by 3, and the set of integers leaving a remainder of 2 when divided by 3 d) the set of integers less than – 100, the set of integers with absolute value not exceeding 100, and the set of integers greater than 100 e) the set of integers not divisible by 3, the set of even integers, and the set of integers that leave a remainder of 3 when divided by 6
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