devarshi-dt-logo

Question:

If S and T are two sets such that S has 21 elements, T has 32 elements, and S∩T has 11 elements, how many elements does S∪T have?

Solution:

Given n(S) = 21, n(T) = 32, n(S∩T) = 11
We know that:
n(S∪T) = n(S) + n(T) - n(S∩T)
∴n(S∪T) = 21 + 32 - 11 = 42
Thus, the set (S∪T) has 42 elements.