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}

Answer 1

(i) {1, 2, 3, …., 10} ≠ {x : x ∈ N and 1 < x < 10}

In the above set according to conditions 1 and 10 excluded.

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

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

In the above set according to conditions,

Set must be {3,5,7,9,.......}.Which is set of odd numbers exluding 1.

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

(iii) {5, 15, 30, 45} ≠ {x : x is a multiple of 15}

In the above set according to conditions 5 must be not in the set.

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

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

 In the above set according to conditions,9 is not prime number.

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

Answer 2

Answer:

(i) {1, 2, 3, …., 10} ≠ {x : x ∈ N and 1 < x < 10}

In the above set according to conditions 1 and 10 excluded.

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

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

In the above set according to conditions,

Set must be {3,5,7,9,.......}.Which is set of odd numbers exluding 1.

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

(iii) {5, 15, 30, 45} ≠ {x : x is a multiple of 15}

In the above set according to conditions 5 must be not in the set.

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

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

 In the above set according to conditions,9 is not prime number.

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

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