Question

Which of the following sets are finite or infinite:
$\left(i\right)$ The set of months of a year
$\left(ii\right)\{1,2,3,...\}$
$\left(iii\right)\{1,2,3,...,99,100\}$
$\left(iv\right)$ The set of positive integers greater than $100$
$\left(v\right)$ The set of prime numbers less than 99

Answer 1

$\left(i\right)$ The set of months of a year is a finite set as it is containing $12$ elements $(i.e.,12$ months$).$

$\left(ii\right)$ Given set $\{1,2,3,...\}$ is an infinite set, because it has infinite number of natural numbers.

$\left(iii\right)$ Since the numbers from $1$ to $100$ are finite. So given set is a finite set.

$\left(iv\right)$ Since the positive integers which are greater than $100$ are infinite. So given set is an infinite set.

$\left(v\right)$ Since the prime numbers which are less than $99$ are countable. So given set is a finite set.