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.
Given a compound logical expression, determine the correct order of operations for constructing the truth table. The connectives, in order of evaluation, are: - \(\cdot\) (AND): Evaluated first. - \(\vee\) (OR): Evaluated next, typically within parentheses. - \(\supset\) (Implication): Evaluated after AND and OR. - \(\equiv\) (Biconditional): Evaluated last.
Step 2: Conclusion. The correct order of operations for the truth table is A, B, C, D.
Final Answer: \[ \boxed{\text{The correct answer is 1. A, B, C, D.}} \]