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GATE | GATE-CS-2005 | Question 8

Last Updated : 28 Jun, 2021
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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?

(A)

X = Y

(B)

X ⊂ Y

(C)

Y ⊂ X

(D)

none of these



Answer: (A)

Explanation:

Answer : (A)
 

Explanation:

The correct answer is (A), X = Y.

Let’s take a look at the sets X and Y again.

  • X = (A – B) – C
    • This means that X is the set of elements that are in A but not in B, and also not in C.
  • Y = (A – C) – (B – C)
    • This means that Y is the set of elements that are in A but not in C, and also not in the set of elements that are in B but not in C.

In other words, X is the set of elements that are in A but not in B and C, and Y is the set of elements that are in A but not in the set of elements that are in B but not in C.

Since X and Y are both the set of elements that are in A but not in B and C, then X = Y.

Therefore, the answer is (A).

Venn diagram

We can solve it by making

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