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+15 votes
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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
in Set Theory & Algebra by Boss (17.5k points)
edited by | 1.3k views
0

 @Akash Kanase or some one

Please comment on below:

+1

@krishn.jh, B-C should be {2}. It will always be equal.

0

Yeah i did mistake there ok 

yes it will be always equal :) @ Shubhgupta thank you

5 Answers

+19 votes
Best answer

 

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

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

So, $X = Y$.

Answer $A$

by Boss (41.9k points)
edited by
0
That's the simple distributive law:

$P*(Q \bigstar R)=(P*Q)\bigstar(P*R)$
0

yes  X= Y here is shaded area :-

+11 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'
by Boss (14.4k points)
0
This should be the accepted answer. Also, there's a slight mistake. It should be $AC'(B'+C)$ instead of $AC'(B+C')$ in the second-last step of Y
+7 votes

From the venn diagram it is clear that, X=Y (Option A)

by Boss (29.2k points)
reshown by
+4 votes

we can also check by taking any three random sets

by Loyal (8.7k points)
+1 vote
Option a ,make venn diagram.
by Active (3.3k points)
Answer:

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