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