Directions: In the question below are given four statements followed by four…
2024
Directions: In the question below are given four statements followed by four conclusions I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.
Statements:
I. Some books are novels.
II. Some novels are poem.
III. All poems are story.
IV. No story is song.
Conclusions:
I. Some songs are books.
II. Some novels are songs.
III. All stories are poem.
IV. No books are song.
- A.
Both II and IV follow
- B.
Only III follows
- C.
Only I follows
- D.
Either I or IV follows
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept: A syllogism conclusion follows only if it holds in every valid Venn diagram consistent with all the given statements — if even one valid diagram breaks it, it does not follow. When neither a ‘Some A are B’ claim nor its exact opposite ‘No A are B’ claim about the very same two sets can be ruled out, but no single diagram forces both to be false together, that pair is called a complementary pair, and by convention exactly one of the pair must be true, so ‘Either...or’ follows for it.
One least-possible diagram consistent with all four statements is shown below:
Building this diagram step by step:
Statement I (some books are novels) makes the Books and Novels circles overlap partially — neither circle contains the other.
Statement II (some novels are poem) overlaps a portion of the Novels circle with the Poems circle; in the least-possible drawing, this poem-linked part of Novels need not be the same part that overlaps Books.
Statement III (all poems are story) places the Poems circle entirely inside the Story circle.
Statement IV (no story is song) keeps the Story and Song circles fully separate, so the Poems circle (already inside Story) is also fully separate from the Song circle.
Because Books connects to the Story-Song side of the diagram only indirectly — through a partial overlap with Novels, and a separate partial overlap of Novels with Poems — no statement fixes whether the Books circle touches the Song circle: a valid diagram can be drawn with them overlapping, and an equally valid diagram can be drawn with them fully apart.
This makes ‘some books are songs’ (Conclusion I, equivalent to ‘some songs are books’) and ‘no books are song’ (Conclusion IV) a genuine complementary pair, so neither is individually certain, but exactly one of the two must hold.
Conclusion II (‘some novels are songs’) is only achievable in some diagrams and never forced in all of them, so it does not follow on its own.
Conclusion III (‘all stories are poem’) reverses Statement III’s one-way containment; a diagram with the Story circle strictly larger than the Poems circle is equally valid, so it does not follow.
Cross-check: Draw a second valid diagram where the Books circle is moved to overlap the Song circle directly, keeping all four statements intact (Books-Novels overlap, Novels-Poems overlap, Poems inside Story, Story-Song separate) — this diagram satisfies Conclusion I. Now draw a third valid diagram where the Books circle is moved fully away from Song, still keeping all four statements intact — this one satisfies Conclusion IV instead. Since both are achievable and neither can be excluded, the complementary-pair rule confirms that only ‘Either I or IV follows’ survives every valid diagram, while the other three options each fail in at least one valid diagram.
Hence, the correct option is ‘Either I or IV follows’.