Question

Verify A-(BNC) = (A - B) U (A - C) using Venn diagrams​

Answer 1

Answer:

Since, A∪B = The total region Covered by both set A and set B

And, A∩B = The common region bounded by set A and set B.

With help of this, we can make the diagram,

By the below diagram 1 ,

A\cup (B\cap C)A∪(B∩C) = The total region of A and B∩C

And, by the diagram 2,

(A\cup B) \cap (A\cup C)(A∪B)∩(A∪C) = The total region of A and B∩C

Thus, AU(B∩C) = (A∪B) ∩ (A∪C)

Hence, proved.

Answer 2

Draw three intersecting circles say A B and C.

Then, for LHS it would be only A excluding the part common in all the three circles, which means the whole A excluding the intersection of all three sets.

Also if you look at RHS, If I take A-B, that means the part of A which is not common with B, and A-C will be the part of A which is not in C. Now on taking union , we will see the same shading in this venn diagram too.

Hence proved