So this is another practice problem I have for discrete math, this time involving compound propositions, with the book my campus uses is Discrete Mathematics with Applications, 7th Edition by Ken Rosen. The problem goes "Let p and q be two given propositions. Use equivalence laws shown in Table 6 and example 3 of section 1.3 to simplify compound propostion $\lnot [p \land (p \to q)]$. Indicate what law(s) you are using in each step."
After trying it on my own, here's what I came up with:
$$\lnot[p \land \lnot(\lnot p \lor \lnot q)]$$ $$\lnot [p \land \lnot(p \land q)]$$ $$\lnot p \lor \lnot [\lnot(p \land q)]$$ $$\lnot p \lor p \land q$$ $$(\lnot p \lor p)\land(\lnot p \lor q)$$ $$T \land(\lnot p \lor q)$$ $$\lnot p \lor q$$
Is this even close to accurate?