GATE CSE 2005 | Question: 8

Question

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?

• A. $X = Y$
• B. $X ⊂ Y$
• C. $Y ⊂ X$
• D. None of these

Comments

 @Akash Kanase or some one

Please comment on below:

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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

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Answer 1

 

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

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

So, $X = Y$.

Answer $A$

Comments

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 :-

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Can X ⊆ Y or Y ⊆ X be the answer of this question?

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$\color{red}{\text{Find Video Solution Below, solved by 3 different methods:}}$

Detailed Video Solution

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Best way

Answer 2

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'

Comments

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

Answer 3

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

Answer 4

we can also check by taking any three random sets