# GATE | GATE-CS-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

Explanation:

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.

Venn diagram

We can solve it by making

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