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 :

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]

${teks-lihat-gambar} afsahsaleem

Other Questions