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De Morgan's Law

If A and B...

Question

If $A$ and $B$ are subsets of a set $X$ , then what is $(A \cap (X - B)) \cup B$ equal to?

A

A \cup B

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B

A \cap B

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C

A

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D

B

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Solution

The correct option is B $A \cup B$
$A \cap (X - B) = A - (A \cap B)$
$A \cap (X - B) \cup B = [A - (A \cap B] \cup B$
$= A \cup B$

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