A young group has 31 members. 15 like skateboarding, 13 like roller skating and 8 don't like either. How many like both?
Solution
Correct Answer: Option B
Let,
people who like skateboarding= n(A)
people who like roller skating= n(B)
and the number of people who like both= n(A ∩ B)
We khow,
n(A U B) = n(A) + n(B) - n(A ∩ B)
⇒n(A U B) = 15 + 13 - n(A ∩ B)
⇒31 - 8 = 15 + 13 - n(A ∩ B)
⇒n(A ∩ B) = 15 + 13 - 23
⇒n(A ∩ B) = 5
Therefore, there are 5 people who like both skateboarding and roller skating.
people who like skateboarding= n(A)
people who like roller skating= n(B)
and the number of people who like both= n(A ∩ B)
We khow,
n(A U B) = n(A) + n(B) - n(A ∩ B)
⇒n(A U B) = 15 + 13 - n(A ∩ B)
⇒31 - 8 = 15 + 13 - n(A ∩ B)
⇒n(A ∩ B) = 15 + 13 - 23
⇒n(A ∩ B) = 5
Therefore, there are 5 people who like both skateboarding and roller skating.
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