Distributive law of set is
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C )
Let us prove it by Venn diagram
Let’s take 3 sets – A, B, C
We have to prove
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
Distributive law is also
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C )
this can also be proved in the same way.
Proof using examples is done here