UGC NET Questions (Paper – 1)

In logic, to say that p implies q is to assert that whenever p is true, q must also be true. This relation is captured formally by the conditional "if p, then q". The guarantee of truth transfer from p to q is the essence of implication. Thus the relation described in the stem is that p implies q.

Option A:
Option A, contradicts, would mean that p and q cannot both be true at the same time, which is the opposite of what is stated. Contradiction signals incompatibility, not guaranteed co-truth. Therefore contradicts is not appropriate.

Option B:
Option B, equals, suggests identity rather than a directional truth-preserving relation. Logical equivalence does require mutual implication, but simple equality does not capture the idea of one truth ensuring another. Hence equals is not the right term here.

Option C:
Option C is correct because implies is the standard expression for a relation where the truth of one statement ensures the truth of another. It is central to conditional logic and validity.

Option D:
Option D, excludes, implies mutual incompatibility or inability to coexist, which again contradicts the idea that the truth of one statement forces the truth of another. Consequently excludes is not suitable.

In propositional logic, the statement “if p, then q” is called a conditional or implication. It asserts that whenever p is true, q must also be true. This relation captures a directed dependence between antecedent and consequent. Therefore the connective in the stem is known as implication.

Option A:
Option A, biconditional, has the form “p if and only if q” and expresses a two-way equivalence. It is stronger than a simple conditional. Thus biconditional does not match the one-way “if p, then q” structure described here.

Option B:
Option B, disjunction, uses “or” to connect two statements and has different truth conditions. It does not encode a directional dependency from p to q. Hence disjunction cannot be the correct answer.

Option C:
Option C properly names implication as the connective that forms a conditional statement from an antecedent and a consequent. Its symbolisation as p → q corresponds exactly to “if p, then q”. Therefore implication is the best choice.

Option D:
Option D, conjunction, joins statements with “and” and requires both to be true. It lacks the conditional structure of premise leading to consequent. So conjunction is not the connective the question refers to.

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.

For a conditional statement p → q, the contrapositive ¬q → ¬p is logically equivalent to the original. Here p is “the number is divisible by 4” and q is “the number is even.” The contrapositive is “if a number is not even, then it is not divisible by 4.” Both the original statement and its contrapositive are true or false together in all possible cases, so they are logically equivalent.

Option A:
Option A reverses the direction of the implication to q → p, which is the converse. The truth of the original statement does not guarantee the truth of its converse; being even does not ensure divisibility by 4.

Option B:
Option B states “If a number is not divisible by 4, then it is not even,” which is the inverse. The inverse is not logically equivalent to the original because many numbers are not divisible by 4 but are still even.

Option C:
Option C correctly expresses the contrapositive ¬q → ¬p: if a number is not even, then it is not divisible by 4. This preserves the logical content of the original implication and is therefore equivalent to it.

Option D:
Option D, “If a number is not divisible by 4, then it is even,” contradicts the original pattern and misstates the relationship between being even and being divisible by 4.

Modus ponens is the basic valid argument form that says: from “If P then Q” and “P,” we may validly infer “Q.” It affirms the antecedent and concludes the consequent. The pattern “If P then Q; P; therefore Q” guarantees that if the premises are true, the conclusion must be true. This is one of the most frequently used inference rules in formal and informal reasoning.

Option A:
Option A presents the correct modus ponens form, with the conditional and affirmation of the antecedent leading to the consequent. It preserves validity in all interpretations.

Option B:
Option B is the fallacy of denying the antecedent: from “If P then Q” and “not P” it draws “not Q,” which is not logically guaranteed, because Q might still be true for other reasons.

Option C:
Option C is the fallacy of affirming the consequent: from “If P then Q” and “Q” it infers “P,” which is also not always valid.

Option D:
Option D is modus tollens, a different but still valid form, which infers “not P” from “If P then Q” and “not Q,” but it is not modus ponens.

Statement A pairs a conditional with its contrapositive, so they are logically equivalent. D is correct because logical equivalence by definition means matching truth values across all valuations. E is also true since a conditional and its contrapositive have identical truth conditions, so if the contrapositive is false, the original conditional must be false. B is wrong because its converse is not always true (an even number need not be divisible by 4), and C is wrong because a conditional is not generally equivalent to its converse. Thus A, D and E only form the correct combination.

Option A:
Option A is correct as it lists precisely the statements that capture equivalence with the contrapositive and the notion of equal truth values, while excluding B and C, which overstate the reliability of converses.

Option B:
Option B is incorrect because it adds B, which asserts that the converse of the divisibility statement is always true, even though simple counterexamples like 6 show this is false.

Option C:
Option C is wrong since it brings in C, which claims conditional and converse are always equivalent, contradicting standard logic, so the combination cannot be correct.

Option D:
Option D is incorrect as it omits A and includes B, thereby dropping a correct contrapositive-equivalence example and admitting a false statement about divisibility.

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.

For an implication "If P, then Q," the contrapositive is "If not Q, then not P." These two statements are logically equivalent, meaning they are either both true or both false in every situation. The contrapositive reverses the direction of the implication and negates both the hypothesis and the conclusion. Therefore, the given statement "If not Q, then not P" is the contrapositive of "If P, then Q."

Option A:
The converse of "If P, then Q" is "If Q, then P," which merely swaps the positions of P and Q without negating them. It is not logically equivalent to the original statement in general. Since the given statement includes negations, it is not the converse.

Option B:
The inverse of "If P, then Q" is "If not P, then not Q," which negates both parts but keeps the order the same. This is different from "If not Q, then not P," which also reverses the roles of P and Q. Thus, the inverse is not the statement described in the question.

Option C:
The contrapositive is correct because it both negates and reverses the components of the original implication, matching the structure "If not Q, then not P." In logical reasoning, proving the contrapositive is a common technique for establishing the truth of an implication. Recognising this form is important for analysing arguments and proofs.

Option D:
A biconditional statement is of the form "P if and only if Q," signifying that P implies Q and Q implies P simultaneously. It does not involve the pattern "If not Q, then not P" as a standalone statement. Therefore, biconditional is not the correct term here.

In logic, implication is a relation where the truth of one statement guarantees the truth of another. If the antecedent is true, the consequent must also be true in a valid implication. This notion underlies conditional statements of the form “if p, then q”. Therefore the relation described in the stem is called implication.

Option A:
Option A, equivalence, is a stronger relation in which each statement implies the other. While equivalence includes two implications, the stem mentions only a one-way guarantee. Hence equivalence is not the most accurate answer.

Option B:
Option B, contradiction, holds when two statements cannot both be true and cannot both be false. This describes incompatibility rather than one statement ensuring another. Thus contradiction does not fit the stem.

Option C:
Option C, contrariety, involves statements that cannot both be true but may both be false. Again, this does not describe a guaranteeing relation. Therefore contrariety is not appropriate here.

Option D:
Option D correctly names implication as the relation in which the truth of one statement leads necessarily to the truth of another. This matches the one-directional assurance expressed in the question.

Statement C is wrong because in standard truth-functional logic the conditional “if p then q” is false precisely when p is true and q is false, not when p is false and q is true. Statements A and B correctly describe the conditions for truth of conjunction and inclusive disjunction, while D accurately explains the biconditional and E states the essential idea that compound truth values depend on component truth values. Hence, C alone is the incorrect statement, so the option that lists only C is correct.

Option A:
Option A is correct since it identifies C as the sole misstatement and implicitly accepts A, B, D and E as standard truth-table definitions. It preserves the conventional semantics of implication while rejecting the inverted condition given in C.

Option B:
Option B is incorrect because it also labels A as wrong, even though A correctly states that “p and q” is true only when both components are true. Treating A as incorrect contradicts the fundamental definition of conjunction.

Option C:
Option C is wrong because it adds D to the set of wrong statements, even though D accurately characterises “if and only if” as true when p and q share the same truth value. Including D among wrong statements undermines correct understanding of biconditional.

Option D:
Option D is also incorrect because by pairing B with C it misclassifies B, which correctly explains that inclusive “or” is false exactly when both disjuncts are false. This combination therefore rejects a correct connective rule.

This option is correct because the symbol '→' represents the logical conditional and is read as "implies." The statement "P → Q" is pronounced "P implies Q." It conveys that whenever P is true, Q must also be true. Therefore, the correct connective word is "implies."

Option A:
The phrase "P causes Q" suggests a causal relationship rather than a logical one. Logical implication does not necessarily assert any physical cause-and-effect link. Thus, "causes" is not the standard reading of the connective.

Option B:
In "P implies Q," "implies" is the accepted wording for the conditional statement. It indicates that truth of P guarantees truth of Q under the logical system. This matches the conventional reading of the symbol '→', so this option is correct.

Option C:
The phrase "P equals Q" refers to equality, which is represented by a different symbol, usually '='. It does not describe a conditional relation where one statement leads to another. Hence, this option is not appropriate.

Option D:
"P contradicts Q" would mean that P and Q cannot both be true, relating to negation rather than implication. That idea is closer to exclusive or or inconsistency, not the ordinary conditional statement. Therefore, this option is incorrect.