Question

If X and Y are two sets and X′ denotes the complement of X, then X ∩ (X ∪ Y)′ is equal to ______.

Options

• X

• Y

• Φ

• X ∩ Y

Answer 1

If X and Y are two sets and X′ denotes the complement of X, then X ∩ (X ∪ Y)′ is equal to Φ.

Explanation:

Let x ∈ X ∩ (X ∪ Y)'

⇒ x ∈ X ∩ (X' ∩ Y')

⇒ x ∈ (X ∩ X') ∩ (X ∩ Y')

⇒ x ∈ Φ ∩ (X ∩ Y')   .....[∵ A ∩ A' = Φ]

⇒ x ∈ Φ