Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All bottles are jugs. Some bottles are flasks. All flasks are bins. Conclusions: I. Some bottles are bins. II. Some jugs are bins. III. Some flasks are jugs.

Correct — A. Rule: the particular statement names a real overlap, and everything true of that overlap is true of both classes it belongs to.

Call the overlap X — the things that are both bottles and flasks.

All flasks are bins, so X is bins. X is bottles, so some bottles are bins — I follows.
All bottles are jugs, so X is jugs. X is bins, so some jugs are bins — II follows.
X is flasks and X is jugs, so some flasks are jugs — III follows.

All three hold, which is option (a).

Why the others are wrong

• (b)
  Only conclusions II and III follow — Leaving out I is the odd omission, because I is the most direct of the three: the bottles that are flasks are bins, since all flasks are bins.
• (c)
  Either conclusion I or II follows — The either-or form applies only when two conclusions cannot both be true but one must be. Here I and II are both true outright, so no either-or arises.
• (d)
  Only conclusions I and II follow — Dropping III misses that the bottle-flask overlap lies inside jugs too, since all bottles are jugs. Those flasks are therefore jugs.

With three statements, start from the particular one. Universal statements alone can never yield a 'some' conclusion, so every valid 'some' here has to trace back to 'Some bottles are flasks'.

Name that overlap and carry it through the universals. Anything the overlap belongs to becomes a valid 'some' conclusion about both of its classes.

Drawing it settles all three at once: jugs is the outer circle, bottles sits wholly inside it, flasks cuts across bottles, and bins contains the whole of flasks.

Key facts

• A valid 'some' conclusion needs a particular statement somewhere in its chain, since universals alone cannot produce one.
• 'Some bottles are flasks' converts, so it also means some flasks are bottles.
• The either-or option applies only to complementary conclusions, where exactly one of the two must be true.

Common traps

• Rejecting conclusion II because no statement links jugs and bins directly
• Reaching for the either-or option whenever two conclusions look related
• Reading 'Some bottles are flasks' as though it also said some bottles are not flasks

No directly related past PYQ was found.