You are given three statements and three conclusions. Choose the comment about…
2018
You are given three statements and three conclusions. Choose the comment about conclusion from the given options below:
Statements:
I. Some pastes are brushes. II. No brush is towel. III. All towels are soaps.
Conclusions:
I. Some soaps are brushes. II. Some pastes are towels. III. No soap is brush.
- A.
Only conclusion I follows
- B.
Only conclusion II follows
- C.
Either I or III follows
- D.
Either II or III follows
Attempted by 28 students.
Show answer & explanation
Correct answer: C
Concept: the Either-Or (complementary pair) rule.
When two offered conclusions share the exact same subject and predicate, and together form an affirmative-particular statement ("Some A are B") and a negative-universal statement ("No A is B") on those same terms, they exhaust every possible relationship between A and B. If the premises leave that specific relationship undetermined — i.e. neither conclusion follows on its own — one of the two must still be true, so “Either…or” is the valid verdict.
Applying it here.
Statement II says brushes and towels have no overlap; statement III says every towel is a soap. So the towel-soaps are guaranteed to exclude brushes.
Nothing in the premises fixes the soaps that are NOT towels — they may or may not overlap with brushes, since only statement I links pastes to brushes, and it says nothing about soaps.
So the soap-brush relationship is genuinely undetermined: a valid diagram can be drawn with some overlap between soaps and brushes, and an equally valid diagram can be drawn with none.
The two conclusions about soaps and brushes are exactly this affirmative-particular / negative-universal pair on the same terms, so together they exhaust the possibilities even though neither follows alone — giving the either-or verdict.
Cross-check.
The conclusion linking pastes and towels uses a different pair of terms altogether (pastes-towels, not soaps-brushes), so it cannot combine with either soap-brush conclusion to form a valid complementary pair — confirming that only the soaps-brushes pairing qualifies for the either-or rule.