# What's wrong with writing the state "x<2 or x>5" as 5<x<2?

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What's wrong with writing the state "x<2 or x>5" as 5<x<2

What's wrong with writing the state "x<2 or x>5" as 5<x<2

##### 2 Answers

See explanation.

#### Explanation:

Those statements describe different sets of numbers:

First one describes numbers which are either less than **or** greater than

#x in (-oo;2) uu (5;+oo)#

The second statement describes numbers which are greater than **and** less than

So the second statement describes an empty set.

**both** **and**

#### Explanation:

There are no values of

For example, if

then

**or**

since only one of the conditions needs to be met for the qualification to be true.