Question

Find the cardinal number of the

If n(B) = 60, n(An B) = 11, and n(A U B) = 105, find n(A).
A. 58
O B. 56
C. 45
D. 54

Answer 1

The cardinal number of set A, given the cardinal numbers of set B, the intersection, and the union of sets A and B is 56.

Step-by-step explanation:

To find the cardinal number of set A, we use the formula for the cardinal number of the union of two sets, which is:

n(A U B) = n(A) + n(B) - n(A ∩ B)

We know that n(A U B) = 105, n(B) = 60, and n(A ∩ B) = 11. Plugging these values into the formula gives us:

105 = n(A) + 60 - 11

Solving for n(A), we get:

n(A) = 105 - 60 + 11

n(A) = 56

Therefore, the correct answer is Option B. 56.

Answer 2

B

Step-by-step explanation:

n(A∪B)=n(A)+n(B)-n(A∩B)

105=n(A)+60-11

n(A)=105-60+11=56