Question

if u is the universal set and A is any set then
UnA=​

Answer 1

Answer:

If U be the universal set and A, B and C are any three finite sets then;

1. If A and B are any two finite sets then n(A - B) = n(A) – n(A ∩ B) i.e. n(A – B) + n(A ∩ B) = n(A)

2. If A and B are any two finite sets then n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

3. If A and B are any two finite sets then n(A ∪ B) = n(A) + n(B) ⇔ A, B are disjoint non-void sets.

4. If A and B are any two finite sets then n(A ∆ B) = Number of elements which belongs to exactly one of A or B

= n((A – B) ∪ (B – A))

= (A – B) + n(B – A) [Since (A - B) and (B – A) are disjoint.]

= n(A) – n(A ∩ B) + n(B) – n(A ∩ B)

= n(A) + n(B) – 2n(A ∩ B)