Prove the distributive law and De Morgan's law.
(i) `A cap (B cup C)=(A cap B)cup(A cap C)`
(ii) `(A cup B)'=A' cap B'`

Explanation

### Step-by-Step Solution

#### Part (i): Proving the Distributive Law

We need to prove that:
\[ A \cap (B \cup C) = (A \cap B) \cup (A \cap C) \]

1. **Assume an element \( x \)**: Let \( x \) be an arbitrary element such that \( x \in A \cap (B \cup C) \).
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