All passing students attend the ceremony. Some ceremony attendees are not in the science track. Which statement must be true?

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Multiple Choice

All passing students attend the ceremony. Some ceremony attendees are not in the science track. Which statement must be true?

The key idea is combining a universal statement with the existence of a group. Saying all passing students attend the ceremony means every member of the passing set is inside the ceremony set. If there are any passing students at all, then at least one passing student must be at the ceremony. In this scenario, we’re intended to assume there are passing students, so there must be some who both pass and attend. That directly makes the statement true: there exist students who pass and attend the ceremony. The fact that some ceremony attendees are not in the science track shows not all attendees are science-track students, so it rules out the possibility that all attendees are science-track. It doesn’t force that there must be science-track attendees, so that option isn’t required. And it contradicts the idea that no passing students attend, since passing students (by assumption) do attend.

The key idea is combining a universal statement with the existence of a group. Saying all passing students attend the ceremony means every member of the passing set is inside the ceremony set. If there are any passing students at all, then at least one passing student must be at the ceremony. In this scenario, we’re intended to assume there are passing students, so there must be some who both pass and attend.

That directly makes the statement true: there exist students who pass and attend the ceremony.

The fact that some ceremony attendees are not in the science track shows not all attendees are science-track students, so it rules out the possibility that all attendees are science-track. It doesn’t force that there must be science-track attendees, so that option isn’t required. And it contradicts the idea that no passing students attend, since passing students (by assumption) do attend.

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