If \(A=\{x\in\mathbb{Z}\mid -3\le x\le 8\}\), \(B=\{x\in\mathbb{Z}\mid 0\le x\le 5\}\), and \(C=\{x\in\mathbb{Z}\mid x\text{ is even}\}\), what is \((A\setminus B)\cap C\)?
Answer and explanation
Correct answer: \(\{-2,6,8\}\)
The set A contains every integer from −3 through 8, while B contains 0, 1, 2, 3, 4, and 5. Removing B from A leaves \(A\setminus B=\{-3,-2,-1,6,7,8\}\). The set C contains all even integers, so we retain only the even members of this difference set. Those are −2, 6, and 8. Hence \((A\setminus B)\cap C=\{-2,6,8\}\). Option B stops before applying the even-number condition.
Frequently asked questions
What is the correct answer to this question?
\(\{-2,6,8\}\)
Why is this the correct answer?
The set A contains every integer from −3 through 8, while B contains 0, 1, 2, 3, 4, and 5. Removing B from A leaves \(A\setminus B=\{-3,-2,-1,6,7,8\}\). The set C contains all even integers, so we retain only the even members of this difference set. Those are −2, 6, and 8. Hence \((A\setminus B)\cap C=\{-2,6,8\}\). Option B stops before applying the even-number condition.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
