If L={x∈N: x is a factor of 17}, what is correct about L?
Answer and explanation
Correct answer: It is a finite set with two elements
The relevant number-theory fact is that 17 is prime. A prime number has exactly two positive factors: 1 and the number itself. Thus the set described is L={1,17}, which contains exactly two elements. It is therefore finite, but it is neither empty nor a singleton. It cannot be infinite because a fixed positive integer has only finitely many positive factors. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
It is a finite set with two elements
Why is this the correct answer?
The relevant number-theory fact is that 17 is prime. A prime number has exactly two positive factors: 1 and the number itself. Thus the set described is L={1,17}, which contains exactly two elements. It is therefore finite, but it is neither empty nor a singleton. It cannot be infinite because a fixed positive integer has only finitely many positive factors. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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