Help with $(P\wedge Q) \vee\neg P \vdash \neg Q \rightarrow \neg P$

Question

$$(P ∧ Q) ∨ ¬P ⊢ ¬Q → ¬P,\qquad P, ¬(¬Q → R) ⊢ ¬(P↔ Q)$$ I am stuck in this, can't wrap my head around it. Need to prove fitch style

Answer 1

The following is one of the Fitch-style proofs that I can think of.

$$\def\fitch#1#2{\quad\begin{array}{|l}#1\\\hline#2\end{array}}\fitch{(P\land Q)\lor\lnot P}{\fitch{P\land Q}{Q\\\fitch{\lnot Q}{\bot\\\lnot P}\\\lnot Q\to\lnot P}\\\fitch{\lnot P}{\fitch{\lnot Q}{\lnot P}\\\lnot Q\to\lnot P}\\\lnot Q\to\lnot P}\qquad\raise{4ex}{\fitch{P\\\lnot(\lnot Q\to R)}{\fitch{P\leftrightarrow Q}{Q\\\fitch{\lnot Q}{\bot\\ R}\\\lnot Q\to R\\\bot}\\\lnot(P\leftrightarrow Q)}}$$

I will leave you to derive the reasoning of each line.