9) For any three sets A, B and C prove using property and NOT BY VENN DIAGRAMA∩(B-C) = (A∩B) - Maths - Sets

Question

9) For any three sets A, B and C prove using property and NOT BY
VENN DIAGRAMA∩(B-C) = (A∩B) – (A∩C)

Ashwini Kumar · Accepted Answer

Let, a∈A∩B-C⇒ a∈A and  a∈B-C                 ⇒  a∈A and  a∈B &  a∉C                 ⇒a∈A & B and a∉A & C                 ⇒ a∈A∩B and a∉A∩C                 ⇒ a∈A∩B-A∩C∴A∩B-C⊆A∩B-A∩C     
1Now let,b∈A∩B-A∩C⇒ b∈A∩B and  b∉A∩C                ⇒ b∈A & B and b∉A & C                ⇒b∈A and  b∈B-C                ⇒ b∈A∩B-C∴A∩B-A∩C ⊆A∩B-C    
2From 1 and 2,A∩B-C=A∩B-A∩C

9) For any three sets A, B and C prove using property and NOT BY VENN DIAGRAMA∩(B-C) = (A∩B) – (A∩C)