Which of the following sets are finite or infinite

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

(i) There are 12 months in a year
Hence, months of a year is a finite set.

(ii) {1, 2, 3 …} has infinity number of elements.
Hence, {1, 2, 3 ...} is a infinite set.

(iii) There are 100 elements in this set.
Hence, {1, 2, 3 …99, 100} is a finite set

(iv) There are infinite Positive integers greater than 100.
Hence, The set of positive integers greater than 100 is an infinite set

(v) there are finite number of prime number less than 99.
Hence, The set of prime numbers less than 99 is a finite set