Question

If n(A – B) = 10, n(B – A) = 23, n(A U B) = 50, then n(A ∩ B) is​

Answer 1

Answer:

n(A ∩ B) = 17

Step-by-step explanation:

We know

n(A - B) + n(A ∩ B)= n(A)  

And, n(B - A) + n(A ∩ B)= n(B)

Also

n( A ∪ B) = n(A) + n(B) - n( A ∩ B)

Using (i) and (ii)

n(A ∪ B) = [n(A - B) + n(A ∩ B)] + [n(B - A) + n(A ∩ B)] - n(A ∩ B)

n(A ∪ B) = n(A - B) + n(B - A) + n(A ∩ B)

Substituting values.

50 = 10 + 23 + n(A ∩ B)

50 = 33 + n(A ∩ B)

n(A ∩ B) = 17

Please list out in the comments if there are any errors in this solution :)