# What is the difference between $\implies$ and $or$?

I was solving a trigonometric equation today and was using the $\implies$ symbol after every step.Seeing this,my instructor advised me not to use this symbol but use $or,$ after every step.He cited that $\implies$ symbol is used majorly in abstract algebra and although there is a very fine difference between the two and may be used interchangebly,it is advised not use it.

But,its not quite clear to me why.Please explain it to me.

For example

I wrote,$\frac{sinAcosB}{cosAsinB}=m\implies\frac{sinAcosB-cosAsinB}{sinAcosB+cosAsinB}=\frac{m-1}{m+1}$...he told me to replace the $\implies$ by $or$...

Thanks in advance for any help!!

• Please give an example. – Eff Sep 12 '16 at 17:28
• The $\Rightarrow$ sign usually means "implies" and so, unless "or" is being used in the sense of "alternatively" it would be incorrect to replace $\Rightarrow$ with "or". However, your use seems sensible to me. – Paul Sundheim Sep 12 '16 at 17:28
• "$\Rightarrow$" doesn't mean "or", "$a\Rightarrow b$" mean "not $a$ or $b$" – Canis Lupus Sep 12 '16 at 17:31
• I suppose "or" is meant in the sense of "in other words"? I'd still prefer "hence", "thus", "therefore", "this implies", "we conclude" – Hagen von Eitzen Sep 12 '16 at 17:34
• @HagenvonEitzen Yes...you understood correctly... – tatan Sep 12 '16 at 17:35

The symbol $\Rightarrow$ is not used any more in abstract algebra than anywhere else, and it is not a reason to avoid using $A \Rightarrow B$. Additionally, "or" doesn't mean the same thing as "implies": indeed, "true or false" is true, while "true implies false" is false.
• I give you an example....I wrote,$\frac{sinAcosB}{cosAsinB}=m\implies\frac{sinAcosB-cosAsinB}{sinAcosB+cosAsinB}=\frac{m-1}{m+1}$...he told me to replace the $\implies$ by $or$... – tatan Sep 12 '16 at 17:36