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: \(A \cap (B \cup C)\)
 
LHS_AN(BUC)_new.svg
 
R.H.S: \((A \cap B)\) \(\cup\) \((A \cap C)\)
 
RHS_(ANB)U(ANC).svg
 
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.