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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