Deductive reasoning starts from a general principle, law or rule and applies it to a particular case to reach a logically necessary conclusion. In mathematical reasoning, most formal proofs are deductive because they proceed from axioms and theorems to specific results. If the premises in a deductive argument are true and the reasoning is valid, the conclusion must be true. This certainty makes deductive reasoning central to mathematical problem solving and theorem proving.
Option A:
Deductive reasoning is correct because it captures the idea of moving from the general to the particular in a logically valid manner. For example, from the general statement "All prime numbers greater than 2 are odd," we can deduce that 11 is odd because it is a prime greater than 2. In UGC NET reasoning questions, recognizing a deductive structure helps evaluate arguments effectively. Thus, this option accurately matches the description in the question.
Option B:
Inductive reasoning moves from specific cases to form a general rule, so it reverses the direction described in the question. For example, observing that several primes are odd and concluding that all primes are odd is an inductive generalization, not an application of a known rule. It provides probable, not certain, conclusions and therefore does not match the definition of moving from general to specific. Hence, it is not the best fit here.
Option C:
Analogical reasoning is based on identifying similarity between two situations and inferring that what is true in one may be true in the other. It does not necessarily begin from a universal rule but from a known case compared to a new case. Because it relies on similarity rather than a general law, it does not guarantee truth of the conclusion. Therefore, it does not describe the general-to-specific pattern mentioned in the question.
Option D:
Abductive reasoning typically involves inferring the most plausible explanation for an observation rather than applying a general rule to a specific case. For instance, seeing that the ground is wet and inferring it has rained is abductive, not deductive. It is often used in hypothesis generation, not in formal mathematical proof. Hence, it does not match the description in the stem.
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