Let's go through the two sections of the questions shown in the image.

SOAL 1:

1. b. Convert the sentence "Kevin sedang mengerjakan PR jika..." into symbolic logic.

   • This is a conditional statement, "Kevin is doing his homework if...". In symbolic logic, "if... then" statements are represented using the implication symbol (→).
   • If we assume:
     • $K$ = "Kevin is doing his homework",
     • $X$ represents the condition or part following "if...",
   • The symbolic representation would be: $X \rightarrow K$.

2. c. Translate the symbolic expression:

   • The given expression is: $\neg q \vee \neg s$.
   • In logic, $\neg$ means "not", and $\vee$ means "or".
   • This translates to: "Either not q or not s". In natural language, it means "q is false or s is false".

SOAL 2:

You are tasked with constructing truth tables for several logical expressions.

1. A. $\neg (\neg p \leftrightarrow q)$

   • The biconditional (↔) means "if and only if," and $\neg$ is the negation.
   • Create a truth table for all possible combinations of $p$ and $q$, calculate $\neg p \leftrightarrow q$, and then negate it.

2. B. $(\neg p \land (\neg q \land r)) \vee (q \land r) \vee (p \land r)$

   • Break down the logical operators and evaluate each part for all combinations of $p, q, r$.

3. C. $(p \land q) \vee \neg (p \vee q)$

   • Calculate $p \land q$, $p \vee q$, and $\neg (p \vee q)$, then evaluate the disjunction.

4. D. $\neg p \land (q \vee \neg r)$

   • Calculate $q \vee \neg r$ and $\neg p$, then evaluate the conjunction.

5. E. $\neg p \vee q \rightarrow \neg q$

   • Treat this as an implication and evaluate the truth values accordingly.

Questions:

1. What is the symbolic form of a biconditional statement in logic?
2. How do you create a truth table for a complex expression involving three variables?
3. What is the difference between $\vee$ (OR) and $\land$ (AND) in logical operations?
4. How would you translate a negation of an entire expression into words?
5. What are the steps to solve an implication statement in symbolic logic?

Tip:

When solving logical problems, always break down complex expressions into smaller parts, and evaluate each step carefully.