Q: Which of the following statements about hypothetical and disjunctive syllogisms are correct?
(A) A hypothetical syllogism involves premises that are conditionals such as βIf p then qβ;
(B) A pure hypothetical syllogism uses only conditionals as premises and conclusion, as in βIf p then q; if q then r; therefore if p then rβ;
(C) A disjunctive syllogism uses a disjunction and the denial of one disjunct to infer the other, as in βp or q; not p; therefore qβ;
(D) Chain reasoning with multiple conditionals can sometimes be represented as a series of modus ponens steps;
(E) All disjunctive syllogisms are invalid simply because they use the connective βorβ;
(F) In UGC NET reasoning, some questions implicitly rely on these patterns even when logical symbols are not explicitly used;
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Q: Which of the following statements about using truth tables in logical reasoning are correct?
(A) Truth tables systematically display all possible truth-value combinations for component statements;
(B) They can be used to test whether a given argument form is valid by checking for rows with true premises and false conclusion;
(C) A statement is a tautology if all entries in its truth table column are true;
(D) For an argument with three distinct propositional variables, a complete truth table will have eight rows;
(E) In UGC NET questions, truth tables are often used implicitly in reasoning even if not drawn explicitly in the exam booklet;
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Q: Which of the following statements about types of inference (pΕ«rvavat, ΕeαΉ£avat, sΔmΔnyato dαΉαΉ£αΉa) in Indian logic are correct?
(A) PΕ«rvavat inference goes from observed cause to unobserved effect, as from dark clouds to impending rain;
(B) ΕeαΉ£avat inference goes from observed effect back to an unobserved cause, as from a flooded river to heavy upstream rain;
(C) SΔmΔnyato dαΉαΉ£αΉa inference is based on general observation not tied to specific causal relations, such as inferring air from motion;
(D) Indian logic recognises only pΕ«rvavat and ΕeαΉ£avat and rejects sΔmΔnyato dαΉαΉ£αΉa as invalid;
(E) UGC NET questions may ask candidates to match examples with these three types of inference;
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Q: Which of the following statements about simple and compound propositions are correct?
(A) A simple proposition contains exactly one logical connective;
(B) Compound propositions are formed by combining simpler propositions with connectives such as βandβ, βorβ or βifβ¦thenβ;
(C) βIt is raining and it is coldβ is a compound proposition built from two simpler ones;
(D) βIt is rainingβ is a compound proposition because it expresses a complete thought;
(E) In UGC NET symbolic logic, identifying simple versus compound statements helps in symbolic translation;
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Q: Select the wrong statement(s) about types of hetvΔbhΔsa (fallacious middle) in Nyaya:
(A) SavyabhicΔra hetu is irregular, because the hetu is present in cases where the sΔdhya is absent;
(B) SatpratipakαΉ£a hetu faces an equally strong counter-reason leading to the opposite conclusion;
(C) BΔdhita hetu is a reason that is contradicted by stronger evidence (e.g., perception), so it cannot establish the sΔdhya;
(D) AsΔdhΔraαΉa hetu is common to many instances and therefore ideal for inference;
(E) In UGC NET, examples may mix different types of hetvΔbhΔsa and ask which label fits best;
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Q: Which of the following statements about using truth tables to test validity are correct?
(A) A truth table can be used to check whether an argument form is valid by seeing if there is any row where all premises are true and the conclusion is false;
(B) If there is a row on the truth table where all premises are true and the conclusion is false, the argument form is invalid;
(C) If there is no row where all premises are true and the conclusion is false, the argument form is valid;
(D) Truth tables can only be used when there is exactly one premise in the argument;
(E) As the number of distinct simple statements increases, the number of rows in the truth table grows exponentially;
(F) For UGC NET Paper 1, candidates are normally expected to construct full truth tables with 64 rows in the exam hall for any complex item;
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