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

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) In R.H.S ‘x’ is greater than 1 and less than 10 but L.H.S is having both 1 and 10. 

ii) L.H.S ≠ R.H.S R.H.S: x = 2n + 1 is definition of odd numbers. L.H.S: Given set is even numbers set. 

iii) x is a multiple of 15. So 5 does not exist.

iv) x is a prime number but 9 is not a prime number.