Question

Let $U$ be the universal set and $A\cup B\cup C=U$. Then $(A–B)\cup (B–C)\cup (C–A){)}^C$ 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 $A\cap B\cap C$


$(A-B)\cup (B-C)\cup (C-A)$
$=(a+f)+(b+d)+(c+e)$
$=a+b+c+d+e+f\therefore \left(\right(A-B)\cup (B-C)\cup (C-A){)}^C=(a+b+c+d+e+f+g)-(a+b+c+d+e+f)=g=A\cap B\cap C$