Question

Which of the following sets is a finite set?

• A. Set of all prime numbers less than $50.$
• B. Set of all prime numbers greater than $50.$
• C. $\{1,3,5,7,...,49,51\}$

Answer 1

Answer: (A), (C)

$\{1,3,5,7,...,49,51\}$

A finite set is a set having finite number of elements.
Here, let's look at the options one by one.

A. Set of all prime numbers less than $50$
We can write this in roster form as:
$A=\{2,3,5,7,...,47\}$

We can count the elements in this set, hence it's a finite set.

B. Set of all prime numbers more than $50.$

We can write this in roster form as:
$B=\{53,57,59,...\}$
Clearly, the caridianality of this set is inifite as the number of elements are not countable.
Hence, it's an infinite set.

C. $\{1,3,5,7,...,49,51\}$

Clearly, this set has countable number of elements and hence this set is a finite set.