Question
For any two sets A and B, $\text{A}\cap\text{(A}\cup\text{B)}'$ is equal to:
- $\text{A}$
- $\text{B}$
- $\phi$
- $\text{A}\cap\text{B}.$
Solution:
$\text{A}\cap\text{(A}\cup\text{B)}'$
$=\text{A}\cap\text{(A}'\cup\text{B}')$ (De Morgen Law)
$=\text{(A}\cap\text{A}')\cap\text{B}'$
$=\phi\cap\text{B}'$
$=\phi$
Hence, the correct answer is option (c).
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
The equations of the lines which pass through the point (3, -2) and are inclined at 60° to the line $\sqrt{3} \text{x} + \text{y} = 1$ is:
$\sqrt{3}\text{x}+\text{y}-\sqrt{3}=0,\sqrt{3}\text{x}-\text{y}-\sqrt{3}=0$
$\sqrt{3}\text{x}+\text{y}+\sqrt{3}=0,\sqrt{3}\text{x}-\text{y}+\sqrt{3}=0$
$\text{x}+\sqrt{3}\text{y}-\sqrt{3}=0,\text{x}-\sqrt{3}\text{y}-\sqrt{3}=0$