Question

Let $U$ be the universal set and$A\cup B\cup C=U.$ Then $\left\{\right(A-B)\cup (B-C)\cup (C-A)\text{'}\}$ 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

The correct option is C

$A\cap B\cap C$

Explanation for the correct option:

Finding the value of $\left\{\right(A-B)\cup (B-C)\cup (C-A)\text{'}\}$:

$(A–B)\cup (B–C)\cup (C–A)$ will majority of the parts except for $A\cap B\cap C$.

So, $\left[\right(A–B)\cup (B–C)\cup (C–A\left)\right]\text{'}=A\cap B\cap C$

Therefore, the correct option is (C)