Question

If $U=\{3,4,5,6,7,8,9\},X=\{3,4\},Y=\{5,6\}$ and $Z=\{7,8,9\}$, then $Y^{\prime }\cap {(X\cap Z)}^{\prime }$ is equal to

• A. $X\cup Y$
• B. $Y\cup Z$
• C. $X^{\prime }\cap Y^{\prime }$
• D. $X\cup Z$

Answer 1

The correct option is D $X\cup Z$

$Y^{\prime }=U-Y=\{3,4,7,8,9\}$
$X\cap Z=0$ as there is no element common in sets X and Z
$\Rightarrow (X\cap Z{)}^{\prime }=U-(X\cap Z)=\{3,4,5,6,7,8,9\}$
Now, $Y^{\prime }\cap (X\cap Z{)}^{\prime }=\{3,4,7,8,9\}\cap \{3,4,5,6,7,8,9\}=\{3,4,7,8,9\}$
This is equal to $X\cup Z=\{3,4,7,8,9\}$