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