   Chapter 1.1, Problem 31E

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# In Exercises 14 − 35 , prove each statement. ( A − B ) ∪ ( A ∩ B ) = A

To determine

To prove: The statement (AB)(AB)=A.

Explanation

Formula Used:

A={xU|xA} where A is the subset of universal set U.

If A and B are two sets then AB is defined as {x|xAandxB}.

If A and B are two sets then AB is defined as {x|xAorxB}.

If A and B are two sets then AB is defined as {x|xAandxB}.

Proof:

Let x(AB)(AB).

Now,

x(AB)(AB)x(AB) or x(AB)

If,

xABxAandxBxA

If,

xABxAandx<

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