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?

We know that

n(S) = 21

n(T) = 32

n(S ∩ T) = 11

It can be written as

n (S ∪ T) = n (S) + n (T) – n (S ∩ T)

Substituting the values

n (S ∪ T) = 21 + 32 – 11

So we get

n (S ∪ T)= 42

Therefore, the set (S ∪ T) has 42 elements.

If A = {x : x ϵ R, x < 5} and B = {x : x ϵ R, x > 4}, find A ∩ B.

Prove that A – B = A ∩ B.’

Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.

Prove that A ∩ (A ⋃ B)’ = ϕ

If A = {3, {2}}, find P(A).