UGCNET Questions

Modus tollens is the valid rule that allows us to infer the negation of the antecedent from a conditional and the negation of its consequent. In symbolic form, from P → Q and ¬Q we conclude ¬P. This pattern preserves validity, because if P had been true, Q would have had to be true as well, so the falsity of Q forces the falsity of P.

Option A:
Option A is modus ponens, which affirms the antecedent to derive the consequent, a different valid pattern.

Option B:
Option B commits the fallacy of denying the antecedent, which is not generally valid.

Option C:
Option C correctly captures the modus tollens form, using the falsity of the consequent to infer the falsity of the antecedent.

Option D:
Option D is the fallacy of affirming the consequent, which is invalid in general.

The phrase “either P or Q, but not both” specifies exclusive disjunction. This means at least one of P or Q is true, and they are not simultaneously true. Symbolically, we combine the inclusive disjunction P ∨ Q with the negation of their conjunction, ¬(P ∧ Q). The conjunction of these two conditions, (P ∨ Q) ∧ ¬(P ∧ Q), precisely encodes exclusivity.

Option A:
Option A, P ∨ Q, is inclusive “or” and allows the possibility that both P and Q are true, which is not allowed in the exclusive reading.

Option B:
Option B adds the restriction that P and Q cannot both hold, yielding the desired “one but not both” condition.

Option C:
Option C, P ∧ Q, demands that both P and Q are true together, the opposite of what exclusivity requires.

Option D:
Option D expresses logical equivalence or biconditional, requiring P and Q to share the same truth value, which is different from exclusive disjunction.

A deductive argument is one in which, if the premises are true, the conclusion must be true. In the metals example, the general premise covers all metals, and the second premise identifies copper as a member of that class. The conclusion about copper’s conductivity follows necessarily from these two claims. There is no room for the conclusion to be false if both premises hold, which is the hallmark of deductive reasoning.

Option A:
Option A uses a classic syllogistic structure: a universal generalisation plus a specific instance leading to a necessity claim. This structure guarantees the conclusion whenever the premises are accepted as true.

Option B:
Option B is inductive because it generalises from sample data to a broader population with only probable support.

Option C:
Option C is a weak inductive prediction based on a single previous observation and does not claim necessity.

Option D:
Option D overgeneralises from one case and therefore is inductive and also fallacious, not deductive.