For T = {x : x is a positive factor of 21}, what is n(T)?
Answer and explanation
Correct answer: 4
The governing concept is cardinality: n(T) is the number of distinct elements in T. A positive factor divides 21 exactly. Since 21=1×21=3×7, its positive factors are 1, 3, 7 and 21. There are four distinct factors, so n(T)=4 and option C is correct. The factors 1 and 21 must not be omitted, and negative factors are excluded by “positive.”
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is cardinality: n(T) is the number of distinct elements in T. A positive factor divides 21 exactly. Since 21=1×21=3×7, its positive factors are 1, 3, 7 and 21. There are four distinct factors, so n(T)=4 and option C is correct. The factors 1 and 21 must not be omitted, and negative factors are excluded by “positive.”
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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