Question

/8. Let U denote the universal set, and A and B be any two sets. If n(U) = 25. n(A) = 17. n(B) = 7
and n(AUB)' = 2, find the following.
(i) n(A)
(ii) n(B)
(iii) n(AUB)
(iv) n(
AB)
(v) n(A-B)
(vi) n(B - A)​

Answer 1

Answer:

Step-by-step explanation:

n(AuB) = n(U) - n(AuB)' = 25 - 2 = 23

n(AuB) = n(A) + n(B) - n(AnB)

n(AnB) = n(A) + n(B) - n(AuB) = 17 + 7 - 23 = 1

i) n(A) = 17

ii) n(B) = 7

iii) n(AuB) = 23

iv) n(AB) = 1

v) n(A-B) = n(A) - n(AnB) = 17 - 1 = 16

vi) n(B-A) = n(B) - n(AnB) = 7 -1 = 6