# If a, b and c are integers, and a < b, then ac < bc. Is the statement true or false?

## Provide proof or a counter example.

Jul 24, 2018

$a < b$
$a \times c < b \times c$
$a c < b c$
Statement is true

#### Explanation:

If $a < b$, and we want to prove whether or not $a c < b c$, then we should start out proof with what we know

We know that $a < b$

We then multiply both sides by $c$ ie $a \times c < b \times c$

Results in $a c < b c$

Therefore, it is true for the statement $a c < b c$ if and only if a,b and" c are integers