Show that the premises “A student in this class has not read the book,” and “Everyone in this class passed the first exam” imply the conclusion “Someone who passed the first exam has not read the book.”
Solution: Let $C(x)$ be “$x$ is in this class”, let $B(x)$ be “$x$ has read the book”, and let $P(x)$ be “$x$ passed the first exam.” The premises are $\exists x\,(C(x) \land \neg B(x))$ and $\forall x\,(C(x) \to P(x))$.
How do I know, judging by the wording, when a premise will be $p \land q$ as opposed to $p \to q$? So in this example, how do I know “A student in this class has not read the book” cannot be $\exists x\,(C(x) \to \neg B(x))$, to say that for some student, if he is in this class, then he has not read the book. I am often wrong in my steps of simplification due to my incorrect interpretation.