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Question

If X and Y are two sets then X(YX) equals
  1. ϕ
  2. none of these
  3. X
  4. Y


Solution

The correct option is A ϕ
Using Venn diagram 


So X(YX) is null set. 

Alternative solution:
X(YX)
X(YX)
(XX)Y
ϕY
ϕ

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