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+9 votes
624 views

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
asked in Set Theory & Algebra by Boss (18k points)
edited by | 624 views

5 Answers

+12 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

answered by Boss (42.4k points)
selected 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 :-

+7 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'
answered by Boss (14.1k points)
+4 votes

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

answered by Loyal (7.9k points)
reshown by
+3 votes

we can also check by taking any three random sets

answered by Loyal (7.7k points)
+1 vote
Option a ,make venn diagram.
answered by Active (3.3k points)


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