Question

If $X$ and $Y$ are two sets and $A\text{'}$ denotes the complement of $A$, then $X\cap (X\cup Y)\text{'}$ is equal to

• A. $X$
• B. $Y$
• C. $\varphi$
• D. $X\cap Y$

Answer 1

The correct option is C $\varphi$

$(X\cup Y)$ is a collection of all the elements of set $X$ and set $Y$.
$(X\cup Y)\text{'}=X^{\prime }\cap Y^{\prime }$ (By De Morgan's Law) or is a collection of all elements which are not in $X$ and not in $Y$.
$(X\cup Y)\text{'}$ has no element common with set $X.$
Hence $X\cap (X\cup Y)\text{'}$ is a null set.