Question

A set X consists of all real numbers greater than or equal to 1. Use set-builder notation to define X.

Answer 1

Theory:

The standard form of set-builder notation is 
 
{ x | “x satisfies a condition” } 

This set-builder notation can be read as “the set of all x such that x (satisfies the condition)”.

For example, { x | x > 0 }  is equivalent to “the set of all x such that x is greater than 0”.

 

Solution:

In the problem, there are 2 conditions that must be satisfied:

1st: x must be a real number

In the notation, this is written as “x ε R”. Where ε means that x is “a member of” and R means “Real number”

 

2nd: x is greater than or equal to 1

This is written as “x ≥ 1”

 

Answer:

Combining the 2 conditions into the set-builder notation:

X = { x | x ε R and x ≥ 1 } 

Answer 2

Answer: $X=\{x\ |\ x\ \epsilon\mathbb{R}\text{ and }x\geq1\}$

Step-by-step explanation:

A set builder notation is used to build or describe the set.

In the given question, there are two conditions on elements of set X that must be satisfied i.e.

For all $x\ \epsilon X$ x belongs to the set of real numbers i.e. $\ x\ \epsilon\ \mathbb{R}$.

For all $x\ \epsilon X$ x

$X=\{x\ |\ x\ \epsilon\mathbb{R}\text{ and }x\geq1\}$