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 pages are diaries. Some diaries are books. All books are notebooks. Conclusions: I. No page is a notebook. II. All pages are notebooks. III. All diaries being notebooks is a possibility.

Correct — D. Read the statements exactly as they stand: every page is a diary, some diaries are books, every book is a notebook.

Conclusion I says no page is a notebook. Not forced — put every page inside the diaries that are also books, and those pages are notebooks.

Conclusion II says all pages are notebooks. Not forced either — put every page inside the diaries that are not books, and nothing connects a page to a notebook.

Conclusion III claims only that all diaries being notebooks is possible. Nothing in the statements forbids it, so the possibility stands.

Only conclusion III follows → option (d).

Why the others are wrong

• (a)
  Both conclusion I and II follow — I and II contradict each other — pages cannot all lie outside notebooks and all inside them. At most one of such a pair can follow, and here neither does.
• (b)
  Only conclusions I and III follow — III is right but I is not. A page may be a notebook: place the pages inside the diaries that are books, and every page becomes one.
• (c)
  Only conclusion II follows — All pages are notebooks needs the pages to lie inside books, which no statement asserts. Some diaries are books leaves room for pages to avoid books entirely.

Syllogism conclusions come in two grades, and the grade decides the test you apply.

A definite conclusion, such as no page is a notebook or all pages are notebooks, must hold in every diagram the statements allow. One counter-diagram kills it.

A possibility conclusion, such as all diaries being notebooks is a possibility, needs only one diagram in which it holds. It is far easier to satisfy, and it is the grade candidates most often reject on sight.

Here the statements leave the pages free to sit inside books or outside them. That freedom kills both definite conclusions and leaves the possibility standing.

Key facts

• A conclusion of the form all X being Y is a possibility follows as soon as one consistent diagram supports it.
• Some diaries are books places no page either inside or outside the books.
• Conclusions I and II here are contradictory, so they cannot both follow.

Common traps

• Rejecting a possibility conclusion because the statements do not assert it, when possibility needs only permission.
• Reading some diaries are books as placing the pages among the books.
• Marking both I and II when the two cannot hold together.

No directly related past PYQ was found.