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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
edited | 709 views
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@Akash Kanase or some one

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

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Yeah i did mistake there ok

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

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

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

So $X = Y$. Answer $A$

edited
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That's the simple distributive law:

$P*(Q \bigstar R)=(P*Q)\bigstar(P*R)$
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yes  X= Y here is shaded area :-

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'

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

reshown

we can also check by taking any three random sets

Option a ,make venn diagram.