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 $n(X \cup Y \cup Z)'$ equals

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

Answer 1

Answer: (D)

$5$

Answer 2

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