Question

Of the 50 entries in a costume contest, 31 entrants were dressed as heroes and 20 entrants were wearing a mask. If 9 entrants were dressed as heroes wearing a mask, how many entrants were neither dressed as heroes nor wearing a mask

Answer 1

8

Explanation:

Given that Of the 50 entries in a costume contest, 31 entrants were dressed as heroes and 20 entrants were wearing a mask. 9 entrants were dressed as heroes wearing a mask.

Let A = heroes and B = wearing mask

n(U) = 50

n(A)=31 and n(B) = 20 and n(AB) =9

Hence n(AUB) =
`31+20-9 = 42`

Persons who were neither dressed as heroes nor wearing a mask

`= n(U)-n(AUB)\\= 50-42=8`