What is "X happens whenever Y happens"?

Question

This page says "$X$ happens whenever $Y$ happens" translates to $Y \implies X$. But I feel $Y\implies X$ allows $X$ to be $True$ when $Y$ is $False$, which does not seem to be correct for "$X$ happens whenever $Y$ happens". I feel it should be $X \Longleftrightarrow Y$. Am I correct with this?

Answer 1

I think this might be more of a language problem than a logic problem. The way I understand the sentence, is:

"Everytime $Y$ happens, $X$ happens also."

Looking at my sentence, it may be more clear why this corresponds to $Y \Rightarrow X$, and not $Y \iff X$. Because $X$ can actually be true while $Y$ is false. I don't say anything about $X$ 'acting' on $Y$.

It is probably the usage of the word 'whenever' that causes a problem. In a way this example shows why one must be careful using language when talking about math / logic, since it is sometimes difficult to be absolutely clear what is meant.

I hope this helps.

Answer 2

Your proposition means that if $ Y $ is true, $ X $ will be certainly true. or in other words, it says that the argument whose premisse is $ Y $ and conclusion is $ X $, is a valid argument.

If $ Y $ is false, we can say nothing about $ X $.

It can be written as $$Y \implies X$$ it is also what we call a conditionnal.