   Chapter 1.1, Problem 33E

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

To determine

To prove: The statement U(AB)=(UA)(UB) where, U is the universal set.

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:

De Morgan’s Laws: For two sets A and B,

(AB)=AB and (AB)=AB.

Consider the LHS of the statement U(AB)=(UA)(UB)

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