Q. 43.6( 24 Votes )

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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}


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