Question

Suppose that n(U) = 200, n(A) = 165, n(B) = 95, and n( A ∩ B ) = 80. Find n( A c ∪ B ).

a. 85
b. 95
c. 15
d. 35
e. 115
f. None of the above.

Answer 1

d) 35

Explanation:

Consider the venn diagram attached below

Given

n(U) = 200

n(A) = 165

n(B) = 95

n(A ∩ B ) = 80

n(
`A^(c)` ∪ B) =?

Using

n(A ∪ B) = n(A) + n(b) - n(A ∩)B

For
`A^(c)`

`n(A^(c)\cup B) = n(A^(C))+ n(B)-n(A^(c)\cap B)---(1)\\n(A^(c))=U-A\\n(A^(c))=n(U)-n(A)\\A^(c)\cap B=B\\n(A^(c)\cap B) =n(B)\\`

Then (1) becomes

`n(A^(c)\cup B) = n(U)-n(A)+ n(B)-n(B)\\n(A^(c)\cup B)=200-165+95-95\\n(A^(c)\cup B)=35`