I came across a proposition which I'm having a hard time converting into predicate logic. It has been a long while since I have touched the topic.
The proposition reads
\begin{align} &\text{Socrates is a human}\\ &\text{Socrates is mortal}\\ &\text{Therefore, some humans are mortal} \end{align}
Using predicate logic, I'd set this up as
\begin{align} &P(s)\\ &M(s)\\ &\exists x\hspace{0.1cm} (P(x) \land M(x)) \end{align}
which can be written as,
$$P(s) \land M(s) \rightarrow \exists x\hspace{0.1cm} (P(x) \land M(x))$$
However, I feel like this is incorrect. Could someone suggest how to better represent this proposition using predicate logic?
I wouldn't try to put these three statements into one statement. A statement is different from an argument. To indicate you are dealing with an argument, you can use the $\therefore$ symbol. So, I would symbolize this argument as: \begin{align} &P(s)\\ &M(s)\\ &\therefore \exists x\hspace{0.1cm} (P(x) \land M(x)) \end{align}