Question

Let n (AUB)=32n(B)=16and n(ANB)9 find n (A)​

Answer 1

32

Explanation:

n(A∪B)=n(A)+n(B)−n(A∩B)−−−−−−−(1)

Given n(A)= ? we represent with x

n(B)= 16

n(A∪B) = 32

Substituting in equation 1 to get n(A)

32 = n(A) + 9 − 9

⇒n(A) = 32 − 0

n(A) = 32

to confirm this we put the values into the formula below

n(A∪B)=n(A)+n(B)−n(A∩B)−−−−−−−(1)

32 = 32 + 9 - 9

Answer 2

n(A) = 25

Explanation:

The relation between cardinality of two sets and that of their union and intersection is ...

n(A∪B) = n(A) +n(B) -n(A∩B)

32 = n(A) +16 -9 . . . . . use the given information

25 = n(A) . . . . . . . . . subtract 7