Question

If $X$ and $Y$ are any two non empty sets then what is ${(X-Y)}^{\prime }$ equal to?

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

Answer 1

The correct option is C $X^{\prime }\cup Y$

$X-Y$ $=\{x:x\in X,x\notin Y\}$
$=\{x:x\in X,x\in Y^{\prime }\}$
$\Rightarrow \{x:x\in X\cap Y^{\prime }\}$
$\Rightarrow {(X-Y)}^{\prime }=(X\cap Y{)}^{\prime }$
= $X^{\prime }\cup \left(Y^{\prime }\right)=X^{\prime }\cup Y$