Question

A statement that is always false regardless of truth values is called______

• A. Contradiction
• B. Tautology
• C. Condition
• D. Implication

Hint:

In mathematics, the "Proof by Contradiction" involves assuming a statement is true and showing that it leads to a logical contradiction, thereby proving the original statement must be false.

Answer 1

The Correct Option is A

Concept: In propositional logic, statements are categorized by the truth values they produce for every possible combination of their atomic variables.
• Tautology: A statement that is always true (e.g., $p \vee \neg p$).
• Contradiction: A statement that is always false (e.g., $p \wedge \neg p$).
• Contingency: A statement that can be true or false depending on the inputs.

Step 1: Defining the nature of a contradiction.
A contradiction is a logical incompatibility between two or more propositions. The resulting column in a truth table for such a statement contains only 'F' (False).

Step 2: Comparing with other terms.
A Tautology (B) is the exact opposite; it results in all 'T' (True). An Implication (D) is just a logical operator ($\rightarrow$), not a classification of a final result.

Step 3: Conclusion.
Based on the definition of a statement that is "always false," Contradiction is the only applicable term.