**Prob. **Prove that-

A∩(B∪C) = (A∩B) ∪ (A∩C)

**Solution:**

Let x ∈ A ∩ (B U C).

Then x ∈ A and x ∈ (B U C).

(x ∈ A and x ∈ B) or (x ∈ A and x ∈ c).

x ∈ (A and B) or x ∈ ( A and c).

x ∈ (A ∩ B) U ( A ∩ C).

**Prob. **Prove that-

A∩(B∪C) = (A∩B) ∪ (A∩C)

**Solution:**

Let x ∈ A ∩ (B U C).

Then x ∈ A and x ∈ (B U C).

(x ∈ A and x ∈ B) or (x ∈ A and x ∈ c).

x ∈ (A and B) or x ∈ ( A and c).

x ∈ (A ∩ B) U ( A ∩ C).

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