Question

If A and B are two sets, then A ∩ (A ∪ B) = ?
1. A
2. B
3. ϕ
4. None of these

Answer 1

Correct Answer - Option 1 : A

Concept:

Distributive law: \(\rm A \cap (B \cup C) = (A \cap B) \cup (A \cap C)\).

Calculation:

According to distributive law: \(\rm A \cap (B \cup C) = (A \cap B) \cup (A \cap C)\)

⇒ \(\rm A \cap (A \cup B) = (A \cap A) \cup (A \cap B)\),

⇒ \(\rm A \cap (A \cup B) = A \cup (A \cap B)\),

⇒ \(\rm A \cap (A \cup B) = A \),

Hence, option 1 is correct.