Q2 of 23 Page 45

Which of the following sets are finite or infinite.

(i) The set of months in a year.


(ii) {1, 2, 3, …, 99, 100}


(iii) The set of prime numbers smaller than 99.

We know that a finite set is the set in which the number of elements of the set are finite and an infinite set is the set in which the number of elements of the set are not finite.


(i) Let ‘M’ be the set of months in a year.


∴ M = {January, February, March, April, May, June, July, August, September, October, November, December}


There are 12 elements in ‘M’.


∴ ‘M’ is finite.


(ii) {1, 2, 3 … 99, 100}


There are 100 elements in the above set.


∴ The given set is finite.


(iii) Let ‘P’ be the set of prime numbers less than 99.


⇒ P = {2, 3, 5, 7, 11 … 89, 97}


There are 25 elements i.e. prime numbers less than 99.


∴ P is finite.


More from this chapter

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4

State the reasons for the following:

(i) {1, 2, 3, …., 10} ≠ {x: x ∈ N and 1 < x < 10}


(ii) {2, 4, 6, 8, 10} ≠ {x: x = 2n + 1 and x ∈ N}


(iii) {5, 15, 30, 45} ≠ {x: x is a multiple of 15}


(iv) {2, 3, 5, 7, 9} ≠ {x: x is a prime number}

 5

List all the subsets of the following sets.

(i) B = {p, q}


(ii) C = {x, y, z}


(iii) D = {a, b, c, d}


(iv) E = {1, 4, 9, 16}


(v) F = {10, 100, 1000}

 1

State which of the following sets are empty and which are not?

(i) The set of lines passing through a point.


(ii) Set of odd natural numbers divisible by 2.


(iii) {x : x is a natural number x < 5 and x > 7}


(iv) {x : x is a common point to any two parallel lines}


(v) Set of even prime numbers.

 3

State whether each of the following sets is finite or infinite.

(i) The set of letters in the English alphabet.


(ii) The set of lines which are parallel to the X-Axis.


(iii) The set of numbers which are multiplies of 5.


(iv) The set of circles passing through the origin (0, 0).