Question

Write each set using set - builder notation

Answer 1

Answer:

A Set is a collection of things (usually numbers).

Example: {5, 7, 11} is a set.

But we can also "build" a set by describing what is in it.

Here is a simple example of set-builder notation:

Set Builder Notation

It says "the set of all x's, such that x is greater than 0".

In other words any value greater than 0

It is also normal to show what type of number x is, like this:

Set Builder Notation

   The member of means "a member of" (or simply "in")

   The reals is the special symbol for Real Numbers.

When we have a simple set like the integers from 2 to 6 we can write:

{2, 3, 4, 5, 6}

But how do we list the Real Numbers in the same interval?

{2, 2.1, 2.01, 2.001, 2.0001, ... ???

So instead we say how to build the list:

{ x member of reals | x ≥ 2 and x ≤ 6 }

Start with all Real Numbers, then limit them between 2 and 6 inclusive.

We can also use set builder notation to do other things, like this:

{ x member of reals | x = x2 } = {0, 1}

All Real Numbers such that x = x2

0 and 1 are the only cases where x = x2

Another Example:

Example: x ≤ 2 or x > 3

Set-Builder Notation looks like this:

{ x member of reals | x ≤ 2 or x >3 }

On the Number Line it looks like:

two intervals

Using Interval notation it looks like:

(−∞, 2]  U  (3, +∞)

Step-by-step explanation:

MARK ME AS BRAINLIEST PLZZZZZZZZZ