Question

Let A and B be two finite sets such that n(A B) = 14 , n(A-B) =26, n(B-A)=46 Find i) n(A) ii) n(B)

Answer 1

GIVEN :

Let A and B be two finite sets such that $n(A\cap B) = 14$ , n(A-B) =26 and n(B-A)=46

TO FIND :

i) n(A)  and ii) n(B)

SOLUTION :

Given that A and B be two finite sets such that $n(A\cap B) = 14$ , n(A-B) =26 and n(B-A)=46

We know that the formula

$n(A-B) = n(A)-n(A\cap B)$

∴ $n(A) = n(A-B) + n(A\cap B)$

Substituting the values we get,

$n(A)= 26+14$

∴ n(A)=40

Similarly, $n(B) = n(B-A) + n(A\cap B)$

n(B)=46+14

∴ n(B)=60

∴ the values are n(A)=40 and n(B)=60.