UGCNET Questions

A necessary condition must be present whenever the outcome occurs. If having a valid admit card is necessary for entry, then anyone who is inside the hall must have such a card. In conditional form this becomes “If a person enters the hall, then the person has a valid admit card.” The statement does not claim that possessing a card alone is enough for entry, only that entry cannot happen without it.

Option A:
Option A treats possessing the card as sufficient for entry, which goes beyond necessity and may ignore other requirements like identity proof.

Option B:
Option B captures the idea that entry implies the presence of the necessary condition, aligning with the logical form “Outcome → Condition.”

Option C:
Option C reverses the direction in a way that ties receiving the card to entering, which is not what the original statement asserts.

Option D:
Option D explicitly mislabels the condition as sufficient but not necessary, contradicting the claim that it is necessary.

Saying that clearing the interview is necessary but not sufficient means that getting the job cannot happen without clearing the interview, yet clearing it alone does not guarantee selection because other criteria may also apply. Logically, this is represented by “If you get the job, then you cleared the interview.” The conditional runs from job to interview, reflecting necessity, not from interview to job, which would indicate sufficiency.

Option A:
Option A wrongly interprets clearing the interview as sufficient and guaranteeing the job, which contradicts the “not sufficient” part of the statement.

Option B:
Option B captures the idea that job selection implies interview clearance, exactly what a necessary condition expresses.

Option C:
Option C denies necessity by allowing job selection without interview clearance, which goes against the original statement.

Option D:
Option D contradicts the problem statement by claiming clearing the interview is neither necessary nor sufficient.

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.

A correct deductive pattern guarantees the truth of the conclusion whenever the premises are true. The form “If it rains, the ground gets wet; it is raining; therefore the ground will get wet” is a classic example of modus ponens. Here the condition and its antecedent are both asserted, making the consequent logically necessary. There is no gap between the premises and the conclusion in such a structure.

Option A:
Option A has the structure “If P then Q; P; therefore Q,” which is modus ponens, a standard valid deductive form where the conclusion necessarily follows if the premises are true.

Option B:
Option B, “The ground is wet, so it must have rained,” affirms the consequent and concludes the antecedent. This is the fallacy of affirming the consequent, because wet ground can have other causes.

Option C:
Option C makes a prediction based on temporal repetition, which is inductive rather than deductive.

Option D:
Option D treats a cloudy sky as a sufficient condition for rain, which is not logically guaranteed and again represents an inductive guess, not a valid deduction.