If P={x:x∈Z, -1≤x≤1}, which statement is correct?
Answer and explanation
Correct answer: P={-1,0,1}
The governing concept is roster representation of an integer-valued set with inclusive bounds. Since x∈Z, only integers are considered, and the inequalities −1≤x≤1 include both endpoints. Listing the integers from −1 through 1 gives −1, 0, and 1. Omitting −1 or 1 would ignore an included boundary, while omitting 0 would ignore an interior integer. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
P={-1,0,1}
Why is this the correct answer?
The governing concept is roster representation of an integer-valued set with inclusive bounds. Since x∈Z, only integers are considered, and the inequalities −1≤x≤1 include both endpoints. Listing the integers from −1 through 1 gives −1, 0, and 1. Omitting −1 or 1 would ignore an included boundary, while omitting 0 would ignore an interior integer. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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