Question

Write the set operation represented by each of these shaded regions of diagrams.

[ Refer The Attachment ]

Note: No Wrong Answer !

Answer 1

Consider fig. (f).

Here the shaded region includes only A∩B and A∩C.

So the union of these two sets is the shaded region, i.e., (A∩B) ∪ (A∩C).

And according to distributive law, we get  (A∩B) ∪ (A∩C) = A∩(B∪C).

Consider fig. (g).

Here the shaded region includes only A∩B and B∩C.

So the union of these two sets is the shaded region, i.e., (A∩B) ∪ (B∩C).

But it will be better to write  (A∩B) ∪ (B∩C)  as  (B∩A) ∪ (B∩C)  according to commutative law.

And according to distributive law, we get  (B∩A) ∪ (B∩C) = B∩(A∪C).

Consider fig. (g).

Here the shaded region includes only A∩C and B∩C.

So the union of these two sets is the shaded region, i.e., (A∩C) ∪ (B∩C).

And according to distributive law, we get  (A∩C) ∪ (B∩C) = (A∪B)∩C  or  C∩(A∪B).