Question

For any two sets A and B, $A\cap \left(A\cup B\right)\text{'}$ is equal to

(a) A (b) B (c) $\varphi$ (d) $A\cap B$

Answer 1

$$\begin{gathered} A\cap \left(A\cup B\right)\text{'} \\ =A\cap \left(A\text{'}\cap B\text{'}\right)\left(\mathrm{De}\mathrm{Morgan}\mathrm{law}\right) \\ =\left(A\cap A\text{'}\right)\cap B\text{'} \\ =\varphi \cap B\text{'} \\ =\varphi \end{gathered}$$

Hence, the correct answer is option (c).