There are 30 members in a community club.
All the members take up at least one activity, either aqua aerobics or pickleball.
There are 15 members who take up aqua aerobics and 24 who take up pickleball.
Given that A = {members who take up aqua aerobics} and P = {members who take up pickleball}
Indicate in the Venn Diagram below, showing clearly, the number of members in each subset.

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Worked solution

7

1. Find the number of members who take up both activities

Since all 30 members take up at least one activity,
n(A∪P)=30.n(A \cup P)=30.
Using
n(A∪P)=n(A)+n(P)−n(A∩P),n(A \cup P)=n(A)+n(P)-n(A \cap P),
30=15+24−n(A∩P).30=15+24-n(A \cap P).
n(A∩P)=39−30=9.n(A \cap P)=39-30=9.

2. Find each region of the Venn diagram

AA only:
15−9=6.15-9=6.

PP only:
24−9=15.24-9=15.

Outside both circles:
30−n(A∪P)=30−30=0.30-n(A \cup P)=30-30=0.

Answer

A∩P=9A \cap P = 9

AA only =6= 6

PP only =15= 15

Outside both circles =0= 0

AI analysis — may contain mistakes.

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