   Chapter 6.3, Problem 7ES ### 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 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, B, and C, ( A − B ) ∩ ( C − B ) = A − ( B ∪ C ) .

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,B and C.

(AB)(CB)=A(BC)

Explanation

Given information:

Let  A,B and C  be any set

Concept used:

:Union of sets:Intersection of sets

: subset of set

Calculation:

Consider the following statement,

“For all sets A,B and C

(AB)(CB)=A(BC)

The objective is to prove the above statement if it is true else provide a counter example.

The above statement is false.

Observe the following counter example,

Let A={x,y,z},B={y,z,w,q},C={x,z,p} be the subsets of a universal set U.

Then,

AB={x,y,z}{y,z,w,q}={x}CB={x,z,p}{y,z,w,q}={x,p}

Thus, (AB)(CB)={x}{x,p}={x}

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