Question

If $A,B$ and $C$ are three subsets of a non-empty set $X$, then $(A^{\prime }\cap B^{\prime }\cap C)\cup (B\cap C)\cup (A\cap C)$ is equal to

• A. $A$
• B. $B$
• C. $C$
• D. $X\cap (A\cup B\cup C)$

Answer 1

The correct option is C $C$

$A^{\prime }\cap B^{\prime }\cap C$ represents the region $\text{(i)}$ only.


From the venn diagram, we can conclude that
$(A^{\prime }\cap B^{\prime }\cap C)\cup (B\cap C)\cup (A\cap C)=C$