Q4 of 23 Page 41

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}

We know that two sets A and B are equal if every element in A belongs to B and every element in B belongs to A.


(i) {x: x ∈ N and 1 < x < 10}


= {2, 3, 4, 5, 6, 7, 8, 9}


But the first set is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}


The second set does not have 1, 10.


∴ {1, 2, 3 … 10} ≠ {x: x ∈ N and 1 < x < 10}


(ii) {x: x = 2n + 1 and x ∈ N}


We know that N = 1, 2, 3, 4 …


Let n = 0, 1, 2, 3 …


∴ When n = 0; x = 2(0) + 1 = 2


When n = 1; x = 2(1) + 1 = 3


When n = 2; x = 2(2) + 2 = 6


When n = 3; x = 2(3) + 2 = 8


When n = 4; x = 2(4) + 2 = 10


∴ Set = {2, 3, 6, 8, 10}


The first given set = {2, 4, 6, 8, 10}


The first set does not have 3.


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


(iii) {x: x is a multiple of 15}


∴ Second set = {15, 30, 45, 60 …}


First set = {5, 15, 30, 45}


The second set does not contain 5.


∴ {5, 15, 30, 45} ≠ {x: x is a multiple of 15}


(iv){x: x is a prime number}


Second set = {2, 3, 5, 7, 11 …}


First set = {2, 3, 5, 7, 9}


The second set i.e. prime number does not contain 9.


∴ {2, 3, 5, 7, 9} ≠ {x: x is a prime number}


More from this chapter

All 23 →
2

Consider the following the following sets and fill up the blank in the statement given below with = or ≠ so as to make the statement true.

A = {1, 2, 3};


B = {The first three natural numbers};


C = {a, b, c, d};


D = {d, c, a, b}


E = {a, e, i, o, u};


F = {set of vowels in English Alphabet}


(i) A ….. B (ii) A ….. E


(iii) C ….. D (iv) D ….. F


(v) F ….. A (vi) D ….. E


(vii) F ….. B

 3

In each of the following, state whether A = B or not.

(i) A = {a, b, c, d}


B = {d, c, a, b}


(ii) A = {4, 8, 12, 16}


B = {8, 4, 16, 18}


(iii) A = {2, 4, 6, 8, 10}


B = {x: x is a positive even integer and x < 10}


(iv)A = {x: x is a multiple of 10}


B = {10, 15, 20, 25, 30, ….}

 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.