GATE 2005

Question 8

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

Engineering-MathematicsSets-And Relation

Question 8 Explanation:

Consider, A = {1, 2, 3, 4, 5, 6}
B = {1, 3, 4, 5}
C = {2, 4, 5, 6}
X = (A – B) – C
X = {2, 6} – {2, 4, 5, 6}
= ∅
Y = (A – C) – (B – C)

= {1, 3} – { 1, 3}
= ∅
X = Y

X = (A – B) – C
= (1, 5) – (5, 7, 4, 3)
= (1)
Y = (A – C) – (B – C)
= (1, 4) – (2, 4)
= (1)
X = Y

Correct Answer: A

Question 8 Explanation:

Consider, A = {1, 2, 3, 4, 5, 6}
B = {1, 3, 4, 5}
C = {2, 4, 5, 6}
X = (A – B) – C
X = {2, 6} – {2, 4, 5, 6}
= ∅
Y = (A – C) – (B – C)

= {1, 3} – { 1, 3}
= ∅
X = Y

X = (A – B) – C
= (1, 5) – (5, 7, 4, 3)
= (1)
Y = (A – C) – (B – C)
= (1, 4) – (2, 4)
= (1)
X = Y

Sohail Kumar

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