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 something is sufficient for an outcome means that whenever that condition holds, the outcome is guaranteed. If having a ticket is sufficient to enter, then anyone with a ticket qualifies for entry, even though there might be other ways to enter in a different system. The correct conditional structure is therefore “If you have a ticket, then you can enter the hall.” This expresses that a ticket alone is enough to ensure entry under the stated rule.

Option A:
Option A reverses the implication and would make having a ticket necessary rather than sufficient, changing the logical direction.

Option B:
Option B preserves the idea that a ticket is an adequate condition that guarantees the possibility of entry today.

Option C:
Option C contradicts the original statement by saying you can enter only without a ticket, which is the opposite of what is meant.

Option D:
Option D claims ticket possession is necessary but not sufficient, which again does not match the explicit statement about sufficiency.

When we say X is necessary for Y, we mean that Y cannot occur without X. Here, the machine working (Y) cannot happen without electricity (X). In conditional form, that becomes: if the machine works, then electricity is present. This does not say that electricity alone is sufficient to make the machine work; it only says that working implies the presence of electricity.

Option A:
Option A correctly reverses the verbal statement into a conditional where the occurrence of machine functioning guarantees that electricity is available. It respects the asymmetry between necessity and sufficiency.

Option B:
Option B treats electricity as sufficient for the machine to work, which is stronger than what “necessary” states and may not be true if other conditions are required.

Option C:
Option C claims that a failure of the machine implies electricity is present, which is unrelated to the notion of electricity being required for proper functioning.

Option D:
Option D contradicts the original statement by saying the machine works even when the necessary condition, electricity, is absent.