Question

Suppose that n(U) = 200, n(A) = 105, n(B) = 110, and n( A ∩ B ) = 30. Find n( A c ∪ B ). a) 80 b) 110 c) 125 d) 95 e) 75 f) None of the above.

Answer 1

Answer:

Option c - $n(A^c\cup B)=125$

Step-by-step explanation:

Given : Suppose that n(U) = 200, n(A) = 105, n(B) = 110, and n(A∩B) = 30.

To find : The value of $n(A^c\cup B)$ ?

Solution :

n(U) = 200, n(A) = 105, n(B) = 110, and n(A∩B) = 30

We know that,

$n(A^c)=n(U)-n(A)$

$n(A^c)=200-105$

$n(A^c)=95$

and $n(A^c \cap B)=n(B)-n(A\cap B)$

$n(A^c \cap B)=110-30$

$n(A^c \cap B)=80$

Now,  $n(A^c\cup B)=n(A^c)+n(B)-n(A^c \cap B)$

$n(A^c\cup B)=95+110-80$

$n(A^c\cup B)=125$

Therefore, option c is correct.

Answer 2

The value of the union set given as n(A^c U B) is; C: 125

What is the union of the set?

We are given;

n(U) = 200, n(A) = 105, n(B) = 110, and n(A ∩ B) = 30.

In sets, we know that complement of set A is;

n(A^c) = n(U) - n(A)

Thus; n(A^c) = 200 - 105

n(A^c) = 95

Also, we know that;

n(A^c ∩ B) = n(B) - n(A ∩ B)

n(A^c ∩ B) = 110 - 30

n(A^c ∩ B) = 80

Thus;

n(A^c U B) = n(A^c) + n(B) - n(A^c ∩ B)

n(A^c U B) = 95 + 110 - 80

n(A^c U B) = 125

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