Question

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

Answer 1

See explanation.

Explanation:

Those statements describe different sets of numbers:

First one describes numbers which are either less than `2` or greater than `5`. In other words it describes interval:

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

The second statement describes numbers which are greater than `5` and less than `2`, but there are no such numbers. If a number is greater than `5` it is also greater than `2`.
So the second statement describes an empty set.

Answer 2

`5 < x < 2` implies that `x` must be both `> 5` and `< 2`

Explanation:

There are no values of `x` which satisfy `5 < x < 2`

For example, if `x=6` so that `5 < x`
then `x cancel(<) 2`

`x < 2` or `x >5` has many solutions
since only one of the conditions needs to be met for the qualification to be true.