   Chapter 6.3, Problem 19ES ### 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
1 views

# For each of 5-21 prove each statement that I 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, P ( A ) ∪ P ( B ) ⊆ P ( A ∪ 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, P(A)P(B)P(AB).

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,

P(A)P(B)P(AB)

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,

P(A)={X|X is a subset of A} and P(B)={X|X is a subset of B}

The sets in P(A)P(B) contains only sets that are subsets of either A and B, and P(AB) contains the elements of both the sets A and B.

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

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