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Question
If A and B are two sets, then A ∩ (A ∪ B) equals ______.
Options
A
B
Φ
A ∩ B
Solution
If A and B are two sets, then A ∩ (A ∪ B) equals A.
Explanation:
Given that: A ∩ (A ∪ B)
Let x ∈ A ∩ (A ∪ B)
⇒ x ∈ A and x ∈ (A ∪ B)
⇒ x ∈ A and (x ∈ A or x ∈ B)
⇒ (x ∈ A and x ∈ A) or (x ∈ A and x ∈ B)
⇒ x ∈ A or x ∈ (A ∩ B)
⇒ x ∈ A.
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