Is $a \le b$ a true statement if $a < b$?

Question

My question is:

Is $a \le b$ true if $a < b$?

For instance: Is $3 \le 4$ a true statement?
I think yes, because $a \le b$ is defined as $a < b\vee a = b$ and this should be true, even if $a = b$ is always false, right?

Thank you very much for your help!
FunkyPeanut

Answer 1

In many cases $a<b$ is defined as saying that $a\le b$ is true and $a\neq b$ is true. Thus if $a<b$ is true, so is $a\le b$.

Answer 2

Indeed it is !!

If $a < b$, then surely $a ≤ b$,

as $≤$ implies less than or equal to. If any one of the conditions, i.e. $<$ or $=$, is true then $a ≤ b$ is true. Therefore $a ≤ b$ will always be true, if $a<b$.