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If $\mathrm{A}$ and $\mathrm{B}$ are two subsets of a set $\mathrm{X}$, then what is $A \cap(A \cup B)^{\prime}$ equal to?
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Verified Answer
The correct answer is:
$\phi$
On applying Demorgan's law, we get
On applying associative law, we get,
$=\left(\mathrm{A} \cap \mathrm{A}^{\prime}\right) \cap \mathrm{B}^{\prime}=\phi \cap \mathrm{B}^{\prime}=\phi$
On applying associative law, we get,
$=\left(\mathrm{A} \cap \mathrm{A}^{\prime}\right) \cap \mathrm{B}^{\prime}=\phi \cap \mathrm{B}^{\prime}=\phi$
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