Question

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

Answer 1

Answer

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}