Question

The universal set, $\xi =\{x:1\le x\le 15\text{and x is an integer}\}$, set $H=\{x:x\text{is a multiple of 3}\}$ and set $K=\{x:x\text{is an even number}\}$. find $n(H^{\prime }\cap K)$

• A. $2$
• B. $5$
• C. $7$
• D. $13$

Answer 1

The correct option is B $5$

Here $\xi =1,2,3,...15$

$H=\{3,6,9,12,15\}$

$K=\{2,4,6,8,10,12,14\}$

The Venn diagram is shown in the figure

Then the set $(H^{\prime }\cap K)$ contains the elements contained in K but not common to H which is $\{2,4,8,10,14\}$.

$\therefore n(H^{\prime }\cap K)=5$