Question

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

Answer 1

`(i)` The set of months of a year - As number of months is always 12, so it will be a final set.
`(ii) {1,2,3...} `- It is a set of all natural numbers which is infinite.
`(iii) {1,2,3,...,99,100}` - It is a set of all natural numbers till 100 as we know the limit. As is a finite set.
`(iv)` 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.
`(v)` 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.