Question

In order to make a truth table for the following statement: \[ P \cdot (Q \vee R) \supset (P \equiv Q) \] if each truth functional connective is represented by the following letters, what would be the correct order of the columns in solving the truth table?
A. \(\cdot\)
B. \(\vee\)
C. \(\supset\)
D. \(\equiv\)
Choose the correct answer from the options given below:

• A. A, B, C, D
• B. B, A, C, D
• C. C, A, D, B
• D. C, B, A, D

Hint:

When constructing truth tables, always follow the hierarchy of logical operations: parentheses, AND, OR, implication, and biconditional.

Answer 1

The Correct Option is A

Step 1: Understanding the statement and truth functional connectives.
We are given a compound logical expression and need to determine the correct order of operations for constructing the truth table. The connectives are: - \(\cdot\) (AND): This operation is evaluated first in the expression. - \(\vee\) (OR): This is used inside the parentheses and should be evaluated next. - \(\supset\) (Implication): This is a conditional operator and follows after the AND and OR. - \(\equiv\) (Biconditional): This is the last operation to evaluate in the statement.
Step 2: Conclusion. The correct order of operations for the truth table is A, B, C, D.
Final Answer: \[ \boxed{\text{The correct answer is 1. A, B, C, D.}} \]