Question

For any three sets A, B and C

A. A ⋂ (B - C) = (A ⋂ B) - (A ⋂ C)

B. A ⋂ (B - C) = (A ⋂ B) - c

C. A ⋃(B - C) = (A ⋃ B) ⋂ (A ⋃C')

D.A ⋃ (B - C) = (A ⋃ B) - (A ⋃ C)

Answer 1

(A⋂B)∖(A⋂C)

= (A⋂B)∖A⋃(A⋂B)∖C (∵ De Morgen’s law with difference and intersection.) 

= ϕ⋃(A⋂B)∖C 

= (A⋂B)∖C 

= A⋂(B∖C) (∵ intersection with difference is difference with intersection)