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.
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