Question

Use set builder notation to describe the set of:

a.) all odd numbers between 100 and 200

b.) all points on the graph of the function y=x^2

Answer 1

a) { x : x = 2n + 1 ∀ n ∈ N where 50 ≤ n ≤ 99 }

b) {(x,y) :
`y=x^2` ∀ x ∈ R, y∈ R}

Explanation:

Set builder form of a set is representation of the set in symbol and word inside {}.

a) All odd numbers between 100 and 200,

∵ every odd number is in the form of 2n + 1 where n ∈ N,

Also, the odd numbers between 100 and 200 are,

101, ....199

If 2n + 1 = 101

⇒ 2n = 100 ⇒ n = 50

If 2n + 1 = 199

⇒ 2n = 198 ⇒ n = 99

Then the set would be,

{ x : x = 2n + 1 ∀ n ∈ N where 50 ≤ n ≤ 99 }

b) All points on the graph of the function
`y=x^2`,

Since, both range and domain of the function are 'Set of all real numbers'

⇒ x ∈ R, y ∈ R,

Also, (x,y) that shows the relation
`y=x^2` will belong to the function,

Hence, the required set builder form would be,

{(x,y) :
`y=x^2` ∀ x ∈ R, y∈ R}