Q3 of 23 Page 45

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).

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 ‘E’ be the set of letters in the English alphabet.


⇒ E = {A, B, C, D … X, Y, Z}


There are 26 alphabets.


∴ E is a finite set.


(ii) Let ‘L’ be the sets of lines which are parallel to X-axis.


Then L is an infinite set.


(iii) Let ‘M’ be the set of multiples of 5.


⇒ M = {5, 10, 15, 20 …}


∴ M is an infinite set.


(iv)Let ‘S’ be the set of circles passing through the origin (0, 0).


Then S is an infinite set.


More from this chapter

All 23 →
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.

 2

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.