https://file.aiquickdraw.com/mathbot/file/1726223028938s5lze4zs.jpg

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.

Buatalah tabel kebenaran simbol logika berikut (logic truth tables), including statements like ¬p, ∧ (and), ∨ (or), ↔ (biconditional), and → (implication).

Learn how to create truth tables for propositional logic, including negation (¬), conjunction (∧), disjunction (∨), biconditional (↔), and implication (→). This guide covers essential logical concepts for students in Grades 10-12 or undergraduate studies.

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