Question

If A has 32 elements ,B has 42 elements and A union B has 62 elements the n(B-A) is

Answer 1

Given,

→  n(A) = 32

→  n(B) = 42

→  n(A ∪ B) = 62

Finding  n(A ∩ B),

    n(A ∩ B) = n(A) + n(B) - n(A ∪ B)

⇒  n(A ∩ B) = 32 + 42 - 62

⇒  n(A ∩ B) = 12

Now,

    n(B - A) = n(B) - n(A ∩ B)

⇒  n(B - A) = 42 - 12

⇒  n(B - A) = 30

Or, the easiest method is,

    n(B - A) = n(A ∪ B) - n(A)

⇒  n(B - A) = 62 - 32

⇒ n(B - A) = 30

Here  n(B)  is not required.

Hence 30 is the answer.