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25 votes
25 votes

Let $E, F$ and $G$ be finite sets. Let

  • $X = (E ∩ F) - (F ∩ G)$ and
  • $Y = (E - (E ∩ G)) - (E - F)$.


Which one of the following is true?

  1. $X ⊂ Y$
  2. $X ⊃ Y$
  3. $X = Y$
  4. $X - Y ≠ \emptyset$ and $Y - X ≠ \emptyset$
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7 Answers

11 votes
11 votes

Let E,F, and G belongs to same universe of discourse U, then we can write  E-F=E ∩ F' =EF' .

X = (E∩F) - (F∩G)  = (E∩F) ∩ (F∩G)' =EF (F' + G') =EFG' =(E ∩F ∩G' )

Y=(E−(E∩G))−(E−F) =E (EG)' - (EF') = E(E'+G') - (EF') = EG' - EF'= EG' (EF')' = EG'(E'+F) =EFG' = (E∩F∩G')

We can clearly see that ,X=Y.

Option (C) X=Y   is the correct answer.

Answer:

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