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 cards are postcards. Some postcards are books. All books are novels. Conclusions: I. Some postcards are novels. II. No card is a book. III. All cards are novels.

Correct — C. Rule: a conclusion follows only if it holds in every arrangement the statements allow.

Some postcards are books, and all books are novels. Those postcards are therefore novels, so conclusion I, some postcards are novels, holds in every case.

Conclusion II, no card is a book, does not follow. All cards are postcards, and nothing stops the cards from sitting inside the part of the postcards that is books.

Conclusion III, all cards are novels, does not follow either. Only some postcards are books, and the cards need not be among those.

One conclusion survives, which is what option (c) says.

Why the others are wrong

• (a)
  Only II and III conclusion follow — Neither II nor III is forced. The statements permit cards to be books, and permit cards to lie outside the novels, so both conclusions fail.
• (b)
  Only I and II conclusion follow — I is sound, but II is only a possibility. No card is a book is one arrangement the statements allow, not one they require.
• (d)
  Only conclusion III follows — III fails and I holds — the wrong way round. All cards are postcards, but only the book part of the postcards is guaranteed to be novels.

Syllogism asks what is forced, not what is likely. A conclusion follows only when no legal diagram of the statements can make it false.

Definite links come from chaining a particular statement with a universal one. Some postcards are books, plus all books are novels, gives some postcards are novels, a definite particular conclusion.

A negative conclusion such as no card is a book can follow only from a premise that is itself negative. These three statements contain no negative at all, so no negative conclusion can be forced.

Key facts

• Some A are B, combined with All B are C, yields Some A are C.
• A negative conclusion cannot follow from two affirmative premises.
• All cards are postcards does not say which part of the postcards the cards occupy.

Common traps

• Treating an arrangement the statements merely allow as a conclusion that follows
• Converting Some postcards are books into All postcards are books
• Reading All cards are postcards backwards as All postcards are cards

No directly related past PYQ was found.