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

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

b) {(x,y) : ∀ x ∈ R, y∈ R}

Step-by-step 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 ,

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 will belong to the function,

Hence, the required set builder form would be,

{(x,y) : ∀ x ∈ R, y∈ R}

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step-by-step explanation: