In the Venn diagram below, shade the region $A' \cap B$. Place the five numbers in their correct positions in the Venn diagram below. 35, 45, 51, 60 and 76 Use ∅, ∈, ∉, ⊂ or ⊄ to complete the statement: 51 ___ B. Answer ...

1. Identify the required set region

$A'$ means all regions not in $A$.

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

2. Shade the correct part of the Venn diagram

Shade only the part of circle $B$ outside circle $A$.

Do not shade the overlap $A \cap B$.

1. Identify the meaning of each set in the Venn diagram

$A$: multiples of $3$

$B$: multiples of $5$

$C$: multiples of $6$, with $C \subset A$

2. Classify the numbers that belong inside the circles

$35$ is a multiple of $5$ only, so it goes in $B$ only.

$45$ is a multiple of $3$ and $5$, but not $6$, so it goes in $A \cap B$ outside $C$.

$51$ is a multiple of $3$ only, so it goes in $A$ only.

$60$ is a multiple of $3$, $5$ and $6$, so it goes in $C \cap B$.

3. Place the number that belongs outside the sets

$76$ is not a multiple of $3$, $5$ or $6$, so it goes outside all the circles, but inside the universal set $\xi$.

1. Determine whether 51 belongs to set B

Set $B$ represents multiples of $5$.

Since $51$ is not a multiple of $5$, $51$ is not an element of $B$.

Therefore,
$51 \notin B$