If country X participates in a particular event, then country Y does not…

Concept: In statement-and-conclusion reasoning built on a mutually exclusive condition ("if A occurs, B does not occur in the same instance"), a valid conclusion must hold in every arrangement consistent with the given data. If one side is known to occupy a fixed share of the total instances, the other side is automatically barred from that same share, so its own share is capped at what remains — but nothing forces it to fill that remaining share completely.

Application: Here, X and Y are mutually exclusive per event — whenever Y participates in an event, X does not participate in that same event. Country Y is given to have participated in 50% of all events, so Country X is automatically excluded from that 50%. That leaves only the remaining 50% of events open to X, and the premises say nothing about how many of those X actually attended — X's participation there can be anywhere from none up to all of that remaining half. The only claim that holds under every such arrangement is that Country X participated in at most 50% of the events.

Cross-check — why each other option fails:

• "Country X did not participate in any event" over-restricts: the premises rule X out of the 50% Y attended, but say nothing that rules X out of the remaining 50% as well, so zero participation is not guaranteed.

• "Country X participated in all the events" is impossible: the events Y attended (50% of the total) are, by the given rule, events X cannot have attended, so X could not have attended every event.

• "Country X participated in at least 50% of the events" cannot be guaranteed: the premises only exclude X from Y's 50%; they place no floor on how many of the other 50% X actually attended, so a guaranteed minimum cannot be concluded.

Result: Country X participated in at most 50% of the events.