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?

Question

Philoid · Accepted Answer

Given-

n(S) = 21, n(T) = 32, and n(S ∩ T) = 11

We know that-

n(S ∪ T) = n(S)+ n(T) - n(S ∩ T)

= 21+32 - 11

= 53 - 11

= 42

∴ n(S ∪ T) = 42

Thus, the no. of elements in n(S ∪ T) is 42.