According to the problem on my homework (yes, this is my homework), number 42 in chapter 2.3 of Discrete Mathematics with Applications by Susanna S. Epp, the following are true: \begin{align} a.)&\:p\vee q \\ b.)&\:q\rightarrow r \\ c.)&\:p\wedge s\rightarrow t\\ d.)&\:\neg\:r\\ e.)&\:\neg\:q\rightarrow u\wedge s\\ f.)&\:\therefore t. \end{align} So I need to prove that $t$ is True. This is my deduction so far: \begin{align} &q\rightarrow r \\ &\neg\:r \\ \therefore\:&\neg\:q \\ &p\vee q \\ &\neg\:q \\ \therefore\:&p \\ &\neg\:q\rightarrow u\wedge s \\ &\neg\:q \\ &u\wedge s \\ &p\wedge s \\ &p\wedge s\rightarrow t \\ \therefore\:&t. \end{align} It seems solid, but I still feel like I'm missing something. Please let me know if you feel this is not a good question, however, as I'm aware of the fact that it is not your job to do my homework. General tips or suggestions would be great.
Thank you for your time,
The conclusion is valid. And you were very careful along the way, which is why I was surprised that you jumped a couple steps when citing $p\land s$.
From $u \land s$, you get $s$ by conditional elimination (simplification). Then you need to use conjunction-introduction to infer $p \land s$.
Apart from that, just as important as writing the steps is writing the justifications. Identify the lines that state a premise (follow each with "Premise"). And after using a rule of inference, cite it as your justification. For example, given premises $p\rightarrow q$ and $p$, you'd write $$ q \tag{modus ponens (conditional elimination)}$$