Answer:
d) 35
Step-by-step explanation:
Consider the venn diagram attached below
Given
n(U) = 200
n(A) = 165
n(B) = 95
n(A ∩ B ) = 80
n([tex]A^{c}[/tex] ∪ B) =?
Using
n(A ∪ B) = n(A) + n(b) - n(A ∩)B
For [tex]A^{c}[/tex]
[tex]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)\\[/tex]
Then (1) becomes
[tex]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[/tex]
