UGCNET Questions

A tautology is a compound proposition that evaluates to true under every possible assignment of truth values to its component propositions. It is logically true by virtue of its form rather than specific factual content. In a full truth table, the column for a tautology’s final result contains only Ts and no Fs. Because of this feature, tautologies play an important role in testing argument forms and deriving equivalences.

Option A:
Option A matches the formal definition of a tautology as a statement that never turns out false in any row of its truth table. It captures the idea of logical necessity independent of empirical facts.

Option B:
Option B describes a contradiction, which is always false and has only Fs in its truth table, the exact opposite of a tautology.

Option C:
Option C refers to a contingency, which is true on some valuations and false on others, so it is neither tautological nor contradictory.

Option D:
Option D suggests that the statement cannot be tested, which is incorrect because tautologies are routinely checked using truth tables and formal methods.

A statement that is always true under every possible assignment of truth values to its components is called a tautology. The disjunction “p or not p” covers all possibilities: if p is true, the first part is true; if p is false, not p is true. Thus, in all cases the compound statement evaluates to true. This makes “p or not p” a classic example of a tautology.

Option A:
Option A, “p and not p,” is instead a contradiction because it asserts that p is both true and false simultaneously. There is no assignment of truth values that can make both p and not p true together, so this statement is never true.

Option B:
Option B, “p or not p,” correctly spans all truth possibilities for p. Since one of p or not p must be true, their disjunction is always true, demonstrating tautological status.

Option C:
Option C, “p → not p,” is not always true. If p is true, the implication would require not p to be true as well, which is impossible, so the statement can be false.

Option D:
Option D, “not p → p,” also fails to be always true; there are assignments where it becomes false, so it is not a tautology.