Question

If A and B are subsets of the universal set

X and n(X) = 50, n(A) = 35, n(B) = 20,

n(A'∩B') = 5, find i) n (A∪B)

ii) n (A∩B) iii) n(A'∩B)

iv) n(A∩B')​

Answer 1

Answer

i) n (A∪B)=45

ii) n (A∩B)=10

iii) n(A'∩B)=10

iv) n(A∩B')=25

Step-by-step explanation:

Given:

n(x)=50

n(A)=35

n(B) = 20

n(A'∩B') = 5

i) n (A∪B)

n (A∪B) = n(x)-n(A'∩B')

=50-5

=45

ii) n (A∩B)

n (A∩B) =n(A)+n(B)-n (A∪B)

=35+20-45

=10

iii) n(A'∩B)

=n(B)-n (A∩B)

=20-10

=10

iv) n(A∩B')

=n(A)-n (A∩B)

=35-10

=25