Valid argument in mathematical reasoning – UGC NET Question

A valid argument is one in which, if the premises are true, the conclusion must be true because of the logical structure. Validity concerns the form of the argument rather than the actual truth of the premises. In mathematical reasoning and proofs, ensuring validity guarantees that no incorrect conclusion is drawn from correct assumptions. Therefore, the phrase "conclusion necessarily follows from the premises" directly describes a valid argument.

Option A:
A sound argument is valid and also has all true premises, which is a stronger condition than mere validity. The question, however, focuses only on the logical relation between premises and conclusion, not on whether the premises are true. Because soundness includes an extra requirement not mentioned, this term does not exactly match the description. Hence, it is not the best answer.

Option B:
A strong argument is a term more often used in inductive reasoning to indicate that the premises provide substantial support for the conclusion, but not certainty. Strength suggests high probability, not logical necessity. Since the question emphasises that the conclusion necessarily follows, "strong" is not the correct technical term.

Option C:
A weak argument gives little support to its conclusion and often suffers from logical gaps or insufficient evidence. It certainly does not guarantee that the conclusion follows from the premises. Thus, it is almost the opposite of what the question describes. Consequently, this option is clearly incorrect.

Option D:
Valid is correct because validity captures exactly the idea that the logical form forces the conclusion to follow from the premises. It does not depend on content but on structure, which is crucial in mathematical proofs and reasoning. Recognising validity helps in evaluating arguments on exams and in solving theoretical problems.