1.

Using the properties of sets and their complements prove thatA ∩ (B − C) = (A ∩ B) - (A ∩ C)

Answer»

Let 

x ∈ {A ∩ (B − C)} 

x ∈ A and x ∈ B and x ∉ C 

(x ∈ A and x ∈ B) and (x ∈ A and  x ∉ C) 

(x ∈ A ∩ B − A ∩ C)

A ∩ (B ∩ C) ⊆ (A ∩ B) − (A ∩ C) …(i) 

Again, let 

y ∈ (A ∩ B) ∩ (A − C) 

y ∈ A and (y ∈ B and y ∉  C) 

y ∈ A and y ∈ B − C 

y ∈ {A ∩ (B − C)} 

(A ∩ B) − (A ∩ C) ⊆ A ∩ (B − C) …(ii) 

From equation (i) and (ii)

we get 

A ∩ (B − C) = (A ∩ B) - (A ∩ C)



Discussion

No Comment Found

Related InterviewSolutions