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

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Answer 1 · 2017-09-13T12:58:16

See explanation.

Explanation:

Those statements describe different sets of numbers:

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

$x \in (- \infty; 2) \cup (5; + \infty)$ $x in (-oo;2) uu (5;+oo)$

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

Answer 2 · 2017-09-13T12:59:07

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

Explanation:

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

For example, if $x = 6$ $x=6$ so that $5 < x$ $5 < x$
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.

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