### Theory:

Verification of distributive property of intersection over union using Venn diagram.

Distributive property of intersection over union: $$A \cap (B \cup C)$$ $$=$$ $$(A \cap B)$$ $$\cup$$ $$(A \cap C)$$

L.H.S: $$A \cap (B \cup C)$$

R.H.S: $$(A \cap B)$$ $$\cup$$ $$(A \cap C)$$

Therefore, the distributive property of intersection over union($$A \cap (B \cup C)$$ $$=$$ $$(A \cap B)$$ $$\cup$$ $$(A \cap C)$$) of three sets $$A$$, $$B$$ and $$C$$ is proved using Venn diagram.