Final answer:
To construct a truth table for the compound statement (p → r) (q → r), list all possible truth values for p, q, and r, determine the truth value for each conditional, and finally, find the truth value of their conjunction.
Step-by-step explanation:
The student has asked to construct a truth table for the compound statement (p → r) (q → r). This involves analyzing the logical relationships between two conditional statements (p → r) and (q → r) and their conjunction.
To create the truth table, we list all possible truth values of the individual propositions p, q, and r. For each combination of truth values, we then determine the truth value of the individual conditional statements and their conjunction.
Steps to Construct the Truth Table:
- Write down all possible combinations of truth values for p, q, and r.
- For each row, calculate the truth value of (p → r) using the rule that a conditional statement is false only when the antecedent is true and the consequent is false.
- Repeat step 2 for (q → r).
- For each row, determine the truth value of the conjunction (p → r) AND (q → r).
The final column of the truth table shows the truth values of the entire compound statement for each combination of p, q, and r.