Question

Given that the universal set, $\xi =\{x:1\le x\le 12\text{and x is an integer}\}$ and the sets $P=\{x:x\text{is a prime number}\},Q=\{x:x\text{is a multiple of 4}\}$ and $R=\{2,3,8,9\}$ the elements of the set $(Q\cup R{)}^{\prime }\cap P$ are

• A. $\{2,3\}$
• B. $\{2,3,5\}$
• C. $\{5,7,11\}$
• D. $\{1,5,7,11\}$

Answer 1

The correct option is C $\{5,7,11\}$

Here $\xi =\{1,2,3,...12\}$

$P=\{2,3,5,7,11\}$

$Q=\{4,8,12\}$

$R=\{2,3,8,9\}$

The Venn diagram is shown in the figure

Then the set $(Q\cup R{)}^{\prime }\cap P$ contains the elements contained in P and neither in $R$ or $Q$ which is same as the elements of $P$ intersection with complement of $R\cup Q$ and it is $\{5,7,11\}$