1.

For any three sets A, B and CA. A ⋂ (B - C) = (A ⋂ B) - (A ⋂ C)B. A ⋂ (B - C) = (A ⋂ B) - cC. A ⋃(B - C) = (A ⋃ B) ⋂ (A ⋃C')D.A ⋃ (B - C) = (A ⋃ B) - (A ⋃ C)

Answer»

(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)



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