   Chapter 6.3, Problem 17ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# For each of 5-21 prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.For all sets A and B, if A ⊆ B then P ( A ) ⊆ P ( B ) .

To determine

To Prove:

For each prove each statement that is true and find a counterexample for each statement that is false. Assume all sets are subsets of a universal set U.

For all sets A and B if AB then P(A)P(B).

Explanation

Given information:

Let  A and B  be any set

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

Consider the following statement,

If AB then P(A)P(B)

The objective is to verify whether the statement is true or not

Recall, the definition for a power set,

A power set is a set of all the subsets of a set.

Let A and B are two sets, then the power sets of A and B are defined by,

Let A and B are two subsets of a universal set U

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