The question in the image asks for a truth table to determine the truth values of a logical expression. The formula in the image can be interpreted as:

Tentukan tabel nilai kebenaran dari:
$(P \land Q) \rightarrow (Q \lor \neg R)$

This logical expression involves three propositions: $P$, $Q$, and $R$, and includes the following operations:

1. $\land$: Logical AND
2. $\lor$: Logical OR
3. $\neg$: Negation
4. $\rightarrow$: Logical implication

Steps to Create the Truth Table:

1. List all possible truth value combinations for $P$, $Q$, and $R$.
2. Compute $P \land Q$.
3. Compute $\neg R$.
4. Compute $Q \lor \neg R$.
5. Compute the final expression: $(P \land Q) \rightarrow (Q \lor \neg R)$.

Let me construct the truth table for this expression. pandas as pd

Define all possible truth values for P, Q, and R

truth_values = [(P, Q, R) for P in [True, False] for Q in [True, False] for R in [True, False]]

Prepare the truth table

data = [] for P, Q, R in truth_values: P_and_Q = P and Q not_R = not R Q_or_not_R = Q or not_R final_result = not P_and_Q or Q_or_not_R # (P ∧ Q) → (Q ∨ ¬R) data.append([P, Q, R, P_and_Q, not_R, Q_or_not_R, final_result])

Create a DataFrame

columns = ["P", "Q", "R", "P ∧ Q", "¬R", "Q ∨ ¬R", "(P ∧ Q) → (Q ∨ ¬R)"] truth_table = pd.DataFrame(data, columns=columns)

import ace_tools as tools; tools.display_dataframe_to_user(name="Truth Table for Logical Expression", dataframe=truth_table)The truth table for the given logical expression has been created. Let me know if you have any questions or need further clarification!

Here are 5 related questions to expand on this topic:

1. What are the key differences between logical conjunction ($\land$) and disjunction ($\lor$) in truth tables?
2. How does the negation ($\neg$) operator affect the truth value of a proposition?
3. Could you explain the behavior of logical implication ($\rightarrow$) in more detail?
4. Can this logical expression be simplified using logical equivalences?
5. How are truth tables used in computer science and digital circuit design?

Tip: Truth tables are a foundational tool for analyzing logical statements and are essential for understanding Boolean algebra and logic gates.