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

Solution: $\left(i\right)$ The set of months of a year - As number of months is always 12, so it will be a final set.
$\left(ii\right)\left\{1,2,3\dots \right\}$- It is a set of all natural numbers which is infinite.
$\left(iii\right)\left\{1,2,3,\dots ,99,100\right\}$ - It is a set of all natural numbers till 100 as we know the limit. As is a finite set.
$\left(iv\right)$ The set of positive integers greater than 100 - As positive integers from 100 are infinite and we do not know the limit, it is an infinite set.
$\left(v\right)$ The set of prime numbers less than 99 - As prime numbers less than 99 are finite and we know the limit of this set, it is a finite set.