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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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Describe two partitions of each of the following sets.

a. { x | x is an integer } b. { a , b , c , d }

c. { 1 , 5 , 9 , 11 , 15 } d. { x | x is a complex number }

(a)

To determine

Two partitions of the set {x|x is an integer .}.

Explanation

Given information:

Set: {x|x is an integer }

Formula used:

1) Partition:

A separation of a non-empty set A into mutually disjoint non-empty subsets is called a partition of set A.

2) Disjoint: Two sets A and B are called disjoint if and only if AB=ϕ.

3) Union:

If A and B are sets, the union of A and B is the set AB ( read as‘ A union B ’) given by

AB={x|xAorxB}.

4) Intersection:

If A and B are sets, the intersection of A and B is the set AB ( read as‘ A intersection B ’) given by, AB={x|xAandxB}.

Explanation:

Let = {x|x is an integer

(b)

To determine

Two partitions of the set {a,b,c,d}.

(c)

To determine

Two partitions of the set {1,5,9,11,15}.

(d)

To determine

Two partitions of the set {x|x is a complex number .}

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