Question

Under short Truth table technique, if the statement is proved false in the first attempt by assigning truth values to the constants, then which possibility of its logical status is eliminated?

• A. Tautologous
• B. Contradictory
• C. Contingent
• D. Tautologous and contingent

Hint:

If a formula becomes false even once, it cannot be a tautology.

Answer 1

The Correct Option is A

Concept:
In truth-functional logic, a statement may be: \[ \text{Tautology} \] \[ \text{Contradiction} \] \[ \text{Contingent} \]

Step 1: Understand tautology.
A tautology is a statement which is true under every possible truth-value assignment. So, if even one assignment makes it false, it cannot be a tautology.

Step 2: Apply the short truth table technique.
The question says the statement is proved false in the first attempt. This means there exists at least one case where the statement is false.

Step 3: Eliminate logical status.
Since a tautology cannot be false in any case, the possibility of being tautologous is eliminated.

Step 4: Final conclusion.
Therefore, the eliminated possibility is: \[ \boxed{\text{Tautologous}} \] Hence: \[ \boxed{\text{(A)}} \]