Direction: Select the option that is true about the Statements and Conclusions…

Concept: a coded statement of the form ‘Only A is B’ translates to the categorical form ‘All B is A’ — every member of B belongs to category A. Given a set of such statements, a conclusion ‘follows’ only when it holds true in every possible Venn-diagram arrangement consistent with the statements; a conclusion holds as a valid ‘possibility’ when at least one such consistent arrangement makes it true, even though it is not forced in every arrangement.

Application: translating the three given statements:

• Only group is single → All single is group.

• Some group is online → group and online share a common region, but the statement never fixes where inside group that region sits.

• Some online is offline → online and offline share a common region.

Conclusion I — ‘No single is online’: since single sits entirely inside group, and the group–online overlap is not pinned to any particular part of group, one valid diagram can draw that overlap away from single (keeping single and online separate), while an equally valid diagram can instead let that overlap fall inside single. Because a universal exclusion between single and online is not forced in every diagram, conclusion I does not follow.

Conclusion II — ‘All single being offline is a possibility’: none of the three statements ties single directly to offline. So a diagram where the whole single subset is drawn inside the offline region is consistent with every statement — nothing forbids it. Since at least one consistent diagram supports it, this possibility conclusion holds.

Cross-check: single and online are linked only through the shared term group, and only by a particular (‘some’) statement — the standard rule is that a particular premise can never force a universal conclusion between the terms it links, matching the finding for conclusion I. Single and offline, by contrast, are not linked by any statement at all — direct or forced — so no statement contradicts a diagram placing single fully inside offline, matching the finding for conclusion II.

Result: only conclusion II follows.