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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?

Compute the truth value of each of the following compound propositions given p, q, and r represent true statements.

Learn how to compute the truth values of compound propositions in propositional logic. This guide covers key logical connectives including disjunction, conjunction, negation, and implication, using truth tables. Suitable for high school students in Grades 10-12.

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