The problem provided is related to propositional logic, specifically testing the validity of arguments using the Truth Table Method (TKP - Tabel Kebenaran Pernyataan). Let's break down the steps for each part and how to approach it.

In each case, we have a set of premises (P1, P2, etc.) and a conclusion (K). To check the validity, we create a truth table to evaluate whether the conclusion is true whenever all premises are true.

Let's break down each subproblem:

a.

Premises:

• P1: $(p \land q) \to (r \land s)$
• P2: $\neg r \lor \neg s$

Conclusion (K):

• $\neg p \lor \neg q$

b.

Premises:

• P1: $\neg ((a \lor b) \to \neg c)$
• P2: $\neg d \lor \neg e \lor \neg c$
• P3: $a \to d$
• P4: $e$

Conclusion (K):

• $b \lor c$

c.

Premises:

• P1: $a \to b$
• P2: $(b \land c) \to d$
• P3: $d$

Conclusion (K):

• $a \land d$

d.

Premises:

• P1: $\neg a \to b$
• P2: $(b \land \neg c) \to \neg d$
• P3: $\neg a$

Conclusion (K):

• $d$

e.

Premises:

• P1: $a \to (\neg b \lor \neg c)$
• P2: $\neg e \to b$
• P3: $\neg a \to d$
• P4: $\neg d$

Conclusion (K):

• $c \to e$

General Approach:

To verify each argument, follow these steps:

1. Construct the truth table with all possible truth values for the variables involved.
2. For each combination of truth values, check the truth values of each premise.
3. Verify whether the conclusion holds whenever all premises are true.
4. If the conclusion is true in all cases where the premises are true, the argument is valid.

Would you like to start with one of these arguments in detail, or would you like a general truth table method explanation for one part? Let me know!

Relative Questions:

1. What is the role of logical connectors (e.g., AND, OR, NOT) in constructing a truth table?
2. How can you identify invalid arguments using the truth table method?
3. What is the significance of testing all possible truth values in a truth table?
4. Can you explain the difference between implication ($\to$) and disjunction ($\lor$) in propositional logic?
5. How does negation impact the truth values of premises and conclusions?

Tip: Always start with simpler arguments when learning truth tables, then gradually handle more complex logical expressions.