Set Notation & Inequalities

Maths: Edexcel A Level Pure Maths, topic 2.3.7

How is Set Notation used with Inequalities?

Set notation can be used to represent the solutions of an inequality.

What is the set notation for an inequality?

What is the set notation for an inequality?

Let's consider the inequality $x>1$ .
The solutions to this inequality are all of the values of $x$ that are greater than 1.
More formally, the solution is the set of all values of $x$ such that $x>1$ .
We can write this as { $x:x>1$ }

What is the set notation for two inequalities?

What is the set notation for two inequalities?

Let's consider the inequalities $x<0$ and $x>2$ .
The solutions to these inequalities are all of the values of $x$ that are less than 0 and greater than 2.
We can also think of the solution as the union of the set of all values of $x$ such that $x<0$ and the set of all values of $x$ such that $x>2$ .

$$x2$$

$x<0$ and $x>2$

We can write this in set notation as:
{ $x:x\lt0$ } ⋃ { $x:x\gt2$ }

What is the set notation for two inequalities?

What is the set notation for two inequalities?

Let's consider the inequality $1 \leq x \leq 3$ .
The solutions to this inequality are all of the values of $x$ that are greater than or equal to 1 and less than or equal to 3.
In set notation we can write this as { $x:1 \leq x \leq 3$ }.

$1 \leq x \leq 3$

$1 \leq x \leq 3$

We can also think of the solution as the intersection of the set of all values of $x$ such that $x\geq1$ and the set of all values of $x$ such that $x\leq3$ .
We can write this in set notation as:
{ $x:x\geq1$ } ∩ { $x:x\leq3$ }

Test yourself on Set Notation & Inequalities

Which of the following shows the set solutions of the inequalities
$x<-2$ and $x>7$ ?

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