How to symbolize the following statement?
Every time it rains I forget my umbrella.
My Attempt:
We can rephrase the given statement as
For every $x$, if $x$ is when it rains then $x$ is when I forget my umbrella.
Let us define \begin{align*} R &: \mbox{ $\ldots$ is when it rains} \\ F &: \mbox{ $\ldots$ is when I forget my umbrella}. \end{align*}
Thus our statement can be symbolized as $$ \forall x \bigl[ R(x) \rightarrow F(x) \bigr]. $$
Is my solution correct?
If not, then how to proceed? What could be our universe of discourse? What should be our predicate(s)?
I think this is great. Another way to do it is in tense logic: $$ G(\phi)\land H(\phi) $$ with $$ \phi\equiv r\rightarrow f. $$ Read this as it is always going to be the case that $\phi$ and it always has been the case that $\phi$. Here you have propositional variables ($r$ and $f$); and semantics consists of a timeline evry point of which validates certain propositional variables.