Four sets of three statements are given below. Suppose these statements are…
2017
Four sets of three statements are given below. Suppose these statements are true even if they differ from known facts. Select the option in which the third statement follows the first two statements.
- A.
All foxes are wild. All jackals are wild. Therefore, all jackals are foxes.
- B.
All fruits are leaves. All flowers are fruits. Therefore, all flowers are leaves.
- C.
All pens are pencils. All rubber are pens. Therefore, all pencils are erasers.
- D.
All buses are roads. All cars are buses. Therefore, all roads are cars.
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Concept:
A categorical syllogism is valid only when its conclusion is forced by its two premises through term chaining. "All A are B" places set A entirely inside set B. When two "All ... are ..." premises share a common middle term, the chain A ⊆ B ⊆ C lets you conclude A ⊆ C — but only in that direction and only for terms that actually appear in the premises.
Two rules decide every such item:
Chain rule — the conclusion must run along the inclusion direction (subset → superset), never reversed.
No new term rule — the conclusion may use only the terms present in the premises; a fresh term that never appeared cannot be concluded.
Application to each set:
foxes ⊆ wild and jackals ⊆ wild: both are inside "wild," but two subsets of the same set need not overlap, so "all jackals are foxes" does not follow.
flowers ⊆ fruits and fruits ⊆ leaves: chaining gives flowers ⊆ leaves, so "all flowers are leaves" follows in the correct direction — this is the valid set.
rubber ⊆ pens ⊆ pencils: the premises never mention "erasers," so concluding anything about erasers breaks the no-new-term rule.
cars ⊆ buses ⊆ roads: this forces "all cars are roads," but the stated conclusion "all roads are cars" reverses the direction (illicit conversion).
Cross-check: Only the flowers–fruits–leaves set keeps both the same terms and the subset → superset direction, confirming it is the one whose third statement is forced by the first two.