Question:
Of the members of three athletic team in a certain school, 21 are in
the Basketball Team, 26 in the Hockey team and 29 in the Football
team. 14 play hockey and basketball, 15 play hockey and football, 12
play football and basketball and 8 play all the three. How many
members are there in all?
Answer:
Let B, H, F denotes the sets of members who are on the basketball team, hockey team and football team respectively.
Now, n(B) = 21
n(H) = 26
n(F) = 29
n(H ∩ B) = 14
n(H ∩ F) = 15
n(F ∩ B) = 12
n(B ∩ H ∩ F) = 8
We have to find the value of n(B ∪ H ∪ F)
Now,
n(B ∪ H ∪ F) = n(B) + n(H) + n(F) + n(H ∩ B) - n(H ∩ F) - n(F ∩ B) = 12 + n(B ∩ H ∩ F)
=> n(B ∪ H ∪ F) = 21 + 26 + 29 - 14 - 15 - 12 + 8
=> n(B ∪ H ∪ F) = 84 - 41
=> n(B ∪ H ∪ F) = 43
So, there are 43 members altogather.
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