$\xi = \{\text{integers } x: 1 \le x \le 12\}$ $A = \{\text{integers } x: 1-2x > -9\}$ $B = \{\text{prime numbers}\}$

1. Identify the universal set and find the elements of set $A$.

$\xi=\{1,2,3,4,5,6,7,8,9,10,11,12\}$

For $A$:
$1-2x>-9$
$-2x>-10$
$x<5$
So, within $\xi$,
$A=\{1,2,3,4\}.$

2. Identify $B'$ and list the elements in $A\cap B'$.

The prime numbers in $\xi$ are
$B=\{2,3,5,7,11\}.$
Hence
$B'=\{1,4,6,8,9,10,12\}.$
Therefore
$A\cap B'=\{1,4\}.$

1. Interpret the set expression and identify the required shaded regions.

$A' \cup B$ means all elements which are not in $A$, or are in $B$.

On the Venn diagram, shade:

• the whole of circle $B$, including $A \cap B$,
• all the region outside circle $A$.

Therefore the only region not shaded is $A \cap B'$, the part inside $A$ but outside $B$.