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If $A$ and $B$ are subsets of a set $X$, then what is $\{A \cap(X-B)\} \cup B$ equal to?
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2531 Upvotes
Verified Answer
The correct answer is:
$A \cup B$
Since, $A$ and $B$ are subsets of set $X$ therefore $A \subseteq X$ and $B \subseteq X$
Consider $\{(A \cap(X-B)\} \cup B$
$=\left(A \cap B^{\prime}\right) \cup B$
$=A \cup B$
$\left(\because B^{\prime} \cap B=B\right)$
Consider $\{(A \cap(X-B)\} \cup B$
$=\left(A \cap B^{\prime}\right) \cup B$
$=A \cup B$
$\left(\because B^{\prime} \cap B=B\right)$
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