Question

if n(A) =10 and n(AnB)=3,find n((AnB) 'nA) .​

Answer 1

Answer:

n(AuB) = n(A) + n (B) -n(AnB) —————-1

We have n(AnB) = 25 and n(A-B) = 18

With these 2 we can calculate n(A)

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

18 = n(A) - 25

=> n(A) = 18 + 25 = 43

now to calculate n(B) we can substitute all the values in equation 1

70 = 43+ n(B) - 25

Answer 2

Answer:

n(A∪ B)= n(A)+ n(B)− n(A∩ B)− −− −− −− (1)

Given

n(A)=

7

n(B)= 9

n(A∪ B)= 14

Substituting in 1

14= 7+ 9− n(A∩ B)

⇒ n(A∩ B)= 16− 14= 2