Question

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.

Answer 1

`a < b`
`atimes c < b times c`
`ac < bc`
Statement is true

Explanation:

If `a < b`, and we want to prove whether or not `ac < bc`, 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 `ac < bc`

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