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)A year contains the following months:

January, February, March, April, May, June, July, August, September, October, November and December.

The total number of months in a year is 12 . Thus, a set of the months in a year has 12 elements in it, which is a finite number.

Hence, it is a finite set.

(ii)Natural numbers: Natural numbers can be defined as all the positive whole numbers.

Some examples of natural numbers are- 1,2,3,4,5,6,7,8,9.... and so on.

As there can be an infinite number of natural numbers, the set consisting of natural numbers would have an infinite number of elements.

Hence,it is an infinite set.

(iii)The given set is defined as:

{ 1,2,3....99,100 }

The elements of the given set contains numbers from 1 to 100 . Thus, the given set has total 100 elements in it, which is a finite number.

Hence, it is a finite set.

(iv) A set of positive integers greater than 100 will be,

{ 101,102,103...... }

The given set can have infinite number of positive integers greater than 100 . Thus, this set contains infinite number of elements.

Hence, it is an infinite set.

(v)A set of prime numbers less than 99 is,

{ 2,3,5,7,11,13,17,19,23,29.....97 }

The given set contains prime numbers between 1 and 99 and has only 25 elements in it.

Hence, the set of prime numbers less than 99 is a finite set.