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Question
If X and Y are subsets of the universal set U, then show that X ⊂ Y ⇒ X ∩ Y = X
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Solution
Note that x ∈ X ∩ Y
⇒ x ∈ X
Thus X ∩ Y ⊂ X
Also, since X ⊂ Y,
x ∈ X
⇒ x ∈ Y
⇒ x ∈ X ∩ Y
So that X ⊂ X ∩ Y
Hence the result X = X ∩ Y follows.
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