Question

Let $U$ be the universal set and $A\cup B\cup C=U$ . Then ${\{(A-B)\cup (B-C)\cup (C-A)\}}^{\prime }$ is equal to

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

Answer 1

Answer: (C)

$A\cap B\cap C$

Refer to the figure attached.

$(A-B)\cup (B-C)\cup (C-A)$ will cover all parts except $A\cap B\cap C$. Hence, $\left[\right(A-B)\cup (B-C)\cup (C-A){]}^{\prime }$ is equal to $A\cap B\cap C$.