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Let $A, B$ and $C$ be non-empty sets and let $X = ( A - B ) - C$ and $Y = ( A - C ) - ( B - C ).$ Which one of the following is TRUE?

  1. $X = Y$
  2. $X ⊂ Y$
  3. $Y ⊂ X$
  4. None of these
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5 Answers

Best answer
37 votes
37 votes

 

$X = (A-B) - C = {1,4} - {4,5,6,7 } = 1$

$Y = (A-C) -(B-C) = {1,2} - {2,3} = 1$

So, $X = Y$.

Answer $A$

edited by
19 votes
19 votes
X=(A-B)-C

=>AB' - C

=>AB'C'

 

Y=(A-C)-(B-C)

=>AC'-BC'

=>AC'(B+C')

=>AC'B'

 

so X=Y

note:P-Q is equivalent to P intersection Q'

or P-Q=PQ'
Answer:

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