If \(A=\{x\mid x\) is an integer and \(0\le x<5\}\) and \(B=\{0,1,2,3,4\}\), which statement is true?
Answer and explanation
Correct answer: \(A=B\)
The integers satisfying \(0\le x<5\) are exactly 0, 1, 2, 3, and 4. Therefore the set-builder description gives \(A=\{0,1,2,3,4\}\), which is precisely the given set \(B\). Thus \(A=B\). Options B and C incorrectly claim a proper-subset relationship, while option D is false because the strict inequality \(x<5\) excludes 5. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(A=B\)
Why is this the correct answer?
The integers satisfying \(0\le x<5\) are exactly 0, 1, 2, 3, and 4. Therefore the set-builder description gives \(A=\{0,1,2,3,4\}\), which is precisely the given set \(B\). Thus \(A=B\). Options B and C incorrectly claim a proper-subset relationship, while option D is false because the strict inequality \(x<5\) excludes 5. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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