Question

Classify $ B = \{ y|y $ is a factor of $ 13\} $ as ‘finite’ or ‘infinite’

Answer 1

Hint: $ a $ is called the factor of $ b $ if $ a $ divides $ b $ . Use this concept to convert the above given set from set builder form to tabular form. Once converted into tabular form, count the number of elements in the set. If the number of elements in the set are finite, then the set is finite. Otherwise the set is infinite.

Complete step-by-step answer:
In set theory, any set which has elements that can be counted and the counting would end at some point are called finite sets.
And the sets, whose elements are either cannot be counted or if counted then the counting will never end are called infinite sets.
For example, we cannot count the number of points on the X-axis. Thus the set of collection of points on the X-axis is uncountably infinite.
And we can count the natural numbers, but we will never see the end of it because, we can always add 1 to the last natural number we counted last and keep on counting the next. Thus, the set of natural numbers is a countably infinite set.
Now, if we use this logic and convert the set B from the set-builder form given above into tabular form. Then we can write it as
 $ \Rightarrow B = \{ 1,13\} $
 $ \Rightarrow n(B) = 2 $
Since, we can count the number of elements in B. it is a ‘finite’ set.
So, the correct answer is “‘finite’ set”.

Note: The set B would have only two elements because 13 is a prime number and primes have only to factors. Namely, 1 and itself. To solve this question, you need to know when a set is called a finite set and what do you mean by the term “factor”.