Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow/s from the given statements. Statements: All pens are pages. Some pages are pins. Some pins are boards. Conclusions: (I) Some pins are pens. (II) Some boards are pages. (III) Some pens are boards.

Correct — A. Rule: a chain breaks at the first Some. From All pens are pages plus Some pages are pins, nothing about pens and pins follows.

Conclusion I, some pins are pens: the pages that are pins may lie wholly outside the pens circle. Not certain.

Conclusion II, some boards are pages: pins link pages and boards, but the pins that are pages and the pins that are boards need not be the same pins. Not certain.

Conclusion III, some pens are boards: this needs both broken links at once, so it is weaker still.

Nothing is forced, so option (a).

Why the others are wrong

• (b)
  Either conclusion I or conclusion III follows. — An either-or verdict needs a complementary pair — two conclusions about the same two terms that cannot both be false. I is about pins and pens, III about pens and boards, so they are not a pair.
• (c)
  Only conclusion I follows. — Some pins are pens would need the pages that are pins to overlap the pens. All pens are pages puts pens inside pages, but says nothing about which stretch of pages the pins touch.
• (d)
  Only conclusion II follows. — Some boards are pages joins two particular statements through pins. Some plus Some yields nothing, because the pins that are pages and the pins that are boards can be entirely separate.

Three statements, and the middle terms decide everything.

A definite conclusion needs the middle term to be fully covered by at least one premise. All pens are pages covers pens, not pages, so the pages that are pins are unconstrained and the chain stops there.

Draw the counter-model rather than the diagram that works. Put the pins touching only the part of pages outside pens, and the boards touching only the part of pins outside pages. Every conclusion fails in that one drawing, which is all a rejection needs.

Key facts

• Two particular premises, both beginning with Some, never yield a definite conclusion.
• All pens are pages places no restriction on which pages the pins overlap.
• An either-or answer requires two conclusions on the same pair of terms that cannot both be false.

Common traps

• Drawing one diagram in which a conclusion holds and calling it proved
• Chaining Some pages are pins with Some pins are boards as though Some were transitive
• Choosing either-or for two conclusions that share only one term

No directly related past PYQ was found.