Q1 of 23 Page 45

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.

We know that an empty set is a finite set. A set which does not contain any element is called an empty set.


(i) Let ‘L’ be the set of lines passing through a point. Then L is infinite. So, it is not an empty set.


(ii) Let ‘O’ be the set of odd natural numbers divisible by 2.


But only even numbers are divisible by 2.


∴ O = ϕ = Empty set


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


⇒ If x < 5 and x > 7, then


⇒ x = ϕ = Empty Set


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


We know that two parallel lines do not intersect. So, there is no common point.


∴ x = ϕ = Empty set


(v) Set of even prime numbers


Let ‘E’ be the set of even prime numbers.


⇒ E = {2} ≠ ϕ


∴ It is not an empty set.


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}

 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.

 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).