On the Venn Diagram shown in the answer space, shade the set $A \cap B'$. $ε = {x: x \text{ is an integer and } 1 \le x \le 100}$ $P = {x: x \text{ is a perfect square}}$ $Q = {x: x \text{ is a multiple of 3}}$ $R = {x: x \text{ is an integer ending in 2}}$ List the elements contained in the set $Q \cap R$. Answer ... Write down $n(P \cap R)$. Answer ...

1. Identify the required Venn diagram region

$A \cap B'$ means elements that are in $A$ and not in $B$.

So shade only the non-overlapping part of circle $A$, leaving the intersection of $A$ and $B$ unshaded.

1. Find the elements that are in both $Q$ and $R$

$Q \cap R$ means the elements common to $Q$ and $R$.

Within $1 \leq x \leq 100$, the integers ending in 2 are
$2, 12, 22, 32, 42, 52, 62, 72, 82, 92$.

The multiples of 3 among these are
$12, 42, 72$.

1. Identify the elements that are both perfect squares and integers ending in 2

Perfect squares from $1$ to $100$ are
$1,4,9,16,25,36,49,64,81,100$.

The only one ending in $2$ is none from this list, but check integers ending in $2$:
$2,12,22,32,42,52,62,72,82,92$.
None of these are perfect squares.

So $P \cap R=\varnothing$.