The problem in the image involves propositional logic, where the task is to compute the truth value of compound propositions involving logical variables $p$, $q$, and $r$, which represent true or false statements.

Key Propositions:

The list contains the following expressions:

31. $(p \lor q) \lor r$
32. $(p \lor q) \land \neg r$
33. $\neg p \land (q \lor r)$
34. $\neg(p \land q) \land r$
35. $\neg(p \implies q) \land \neg r$
36. $\neg[(p \lor q) \implies r]$
37. $p \lor (q \implies \neg r)$
38. $\neg[\neg p \implies (q \implies \neg r)]$

These are various logical connectives including disjunction ( $\lor$ ), conjunction ( $\land$ ), implication ( $\implies$ ), and negation ( $\neg$).

The user has attempted truth tables for these logical propositions.

Steps for Calculation:

To compute the truth value of these expressions, you need the truth values of $p$, $q$, and $r$. From the given problem, these are assumed to represent true or false statements, typically starting with all combinations of $p$, $q$, and $r$.

Would you like me to walk through any specific proposition(s) from the list or explain the method of evaluating truth tables for these expressions?