Deductive proof construction I have for a long time having hard to understand how to create correct deductive proofs. I have been working on trying to solve examples but I don't really know how to proceed. 

If we for instance have the argument: (A∧C)′∧C → (B∨C)∧A′
and have a list of equivalences and inference rules, how do I use the list in order to make hypotheses of the argument?

The inference rules are impl, dn, symm, de morgan, mp, mt, conj, add.
Normally you try to see if the statement you would like to prove is equivalent to a tautology. Like the following:

$$\begin{align}
&amp;(A\wedge C)'\wedge C \rightarrow (B\vee C)\wedge A'\\
\Leftrightarrow &amp; [(A\wedge C)'\wedge C]' \vee [(B\vee C)\wedge A']\\
\Leftrightarrow &amp; (A\wedge C)\vee C' \vee [(B\vee C)\wedge A']\\
\Leftrightarrow &amp; (A\wedge C)\vee C' \vee (B\wedge A') \vee (C\wedge A')\\
\Leftrightarrow &amp; [C \wedge(A \vee A')] \vee C' \vee (B\wedge A')\\
\Leftrightarrow &amp; C \vee C' \vee (B\wedge A')\\
\Leftrightarrow &amp; True\\
\end{align}$$

If you would like to write in a better way, write this backward, from $C \vee C' \vee (B\wedge A')$ up to $\Leftrightarrow (A\wedge C)'\wedge C \rightarrow (B\vee C)\wedge A'$.
Here is the OP's question:


  If we for instance have the argument: (A∧C)′∧C → (B∨C)∧A′ and have a list of equivalences and inference rules, how do I use the list in order to make hypotheses of the argument?


Given a goal to derive in propositional logic, perhaps some premises that one may assume, and permitted inference rules the question appears to be: How should one construct a derivation leading to the goal?

One approach is to let a proof checker guide one through the proof by specifying the permitted rules, optionally checking each step, and verifying that the proof is correct when the goal has been reached.  

Here is a proof of the example offered by the OP using such a proof checker:



With a proof checker to guide one, this hopefully makes the task of learning how to write such proofs manageable. To see if one understands how this is done, one can try entering the above proof into the proof checker, line-by-line, to see if one gets the same result. 



Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/

P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Fall 2019. http://forallx.openlogicproject.org/forallxyyc.pdf