Four sets of three statements each are given below. Take these statements to…
2017
Four sets of three statements each are given below. Take these statements to be true even if they look factually absurd. Select one alternative in which third statement is implied by the first two statements.
- A.
All bats are balls. All stumps are bats. Therefore, all balls are stumps.
- B.
All fruits are flowers. All vegetables are fruits. Therefore all vegetables are flowers.
- C.
All trains are buses. All buses are roads. Therefore, all roads are buses.
- D.
All R's are T's. All T's are Q's. Therefore, all Q's are R's.
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Concept
A categorical syllogism of the form "All A are B" and "All B are C" lets you validly conclude "All A are C" — the subset relation is transitive: A is inside B, and B is inside C, so A must be inside C. The direction matters: you may chain forward through the middle term, but you may NOT reverse a universal statement. From "All X are Y" it does not follow that "All Y are X" (that is illicit conversion).
Application
Examine the pair "All vegetables are fruits" and "All fruits are flowers." Here the middle term is "fruits": vegetables sit inside fruits, and fruits sit inside flowers. Chaining forward, vegetables must sit inside flowers, so "All vegetables are flowers" is a valid conclusion that follows directly from the two premises. The conclusion keeps the same subject-to-predicate direction as the premises, so nothing is reversed.
Cross-check / Contrast
Each of the other three sets draws a conclusion that reverses one of its premises, which is the classic illicit-conversion error:
From "All bats are balls" and "All stumps are bats," the only valid conclusion is "All stumps are balls." Concluding "All balls are stumps" reverses the chain and is invalid.
From "All trains are buses" and "All buses are roads," the valid conclusion is "All trains are roads." Concluding "All roads are buses" reverses "All buses are roads" and is invalid.
From "All R are T" and "All T are Q," the valid conclusion is "All R are Q." Concluding "All Q are R" reverses the chain and is invalid.
Only the vegetables-fruits-flowers set chains the middle term forward without reversal, so it is the alternative whose third statement is genuinely implied by the first two.