Question

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

Answer 1

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

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\}`

Answer 2

Theory:

The standard form of set-builder notation is

“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 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