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?

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?

Answer
It is given that
n(S) = 21, n(T) = 32 and n(S ∩ T) = 11
use formula
n (S ∪ T) = n (S) + n (T) - n (S ∩ T)
plug the values we get.
n (S ∪ T) = 21 + 32 - 11 = 42
Hence, the set (S ∪ T) has 42 elements.