Question

Let $X$, $Y$, $Z$ be subsets of $U$, where $n(U)=35$, $n(X)=15$, $n(Y)=22$, $n(Z)=14$ and $n(X\cap Y)=11$, $n(Y\cap Z)=8$, $n(X\cap Z)=5$, $n(X\cap Y\cap Z)=3$ then $n(X\cup Y\cup Z{)}^{\prime }$ equals

• A. $35$
• B. $30$
• C. $26$
• D. $5$

Answer 1

Answer: (D)

We know that $n(X\cup Y\cup Z)=n(X)+n(Y)+$
$n(Z)-n(X\cap Y)-n(Y\cap Z)-n(X\cap Z)+n(X\cap Y\cap Z)$
$=(15+22+14)-(11+8+5)+3=30$
$\therefore n(X\cup Y\cup Z{)}^{\prime }=n(U)-n(X\cup F\cup Z)=35-30=5$