# Show that if A,b, and C are sets, then a) by showing each

## Problem 17E Chapter 2.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition

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Problem 17E

Show that if A,b, and C are sets, then

a) by showing each side is a subset of the other side.

b) using a membership table.

Step-by-Step Solution:

Step 1:

In this problem we have to show that  by  each side is a subset of the other side.

Step 2: some definitions

Union: the union of the sets A and B , denoted by , which is the set that contains those element that are either in A or in B , or in both.

Therefore     = { }.

Intersection : the intersection of the sets A and B , it is denoted by , which is the set containing those elements in both A and B.

Therefore    .

Complement: let U is the universal set and A be any set then the complement of A , denoted by , that it is a set of elements not in A.

i.e.

Step 3 of 4

Step 4 of 4

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