Question

Verify AU(BnC)=(AUB)n(AUC) using Venn diagrams

Answer 1

In the attachment I have answered this problem.

From (1) and (2) it is clear that

AU(BnC) = (AUB)n(AUC)

See the attachment for detailed solution.

Answer 2

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 ,

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

And, by the diagram 2,

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

Thus, AU(B∩C) = (A∪B) ∩ (A∪C)

Hence, proved.