Statements: Some bricks are trees. All trees are pens. All pens are boats.…
2023
Statements: Some bricks are trees. All trees are pens. All pens are boats.
Conclusions:
Some boats are bricks.
Some pens are bricks.
Some trees are bricks.
Some bricks are boats.
- A.
Only I and II follow
- B.
Only III and IV follow
- C.
None follows
- D.
All follow
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept: A statement of the form "Some A are B" (a particular affirmative) always converts simply — it is logically equivalent to "Some B are A". Separately, when a particular affirmative premise ("Some A are B") shares its predicate term with a universal affirmative premise ("All B are C"), the two combine validly into "Some A are C". This chaining pattern can be re-applied again through a further universal premise that shares a term with the newly reached "Some…are…" statement — there is no cap on how many premises may be linked in sequence.
Application, step by step:
Start from the given premise: Some bricks are trees.
Combine it with All trees are pens (shared term: trees) to get: Some bricks are pens.
Combine Some bricks are pens with All pens are boats (shared term: pens) to get: Some bricks are boats.
Convert each reached "Some X are Y" statement to its equivalent "Some Y are X" form: Some bricks are trees converts to Some trees are bricks; Some bricks are pens converts to Some pens are bricks; Some bricks are boats converts to Some boats are bricks.
Cross-check (Venn view): since All trees are pens and All pens are boats, every tree is also a pen and a boat. The premise Some bricks are trees says the brick–tree overlap region is non-empty; that same region therefore also lies inside pens and inside boats. So this one overlapping region simultaneously touches bricks, trees, pens, and boats — which is exactly what each of the four listed statements below claims.
Statement | Wording | How it follows |
|---|---|---|
I | Some boats are bricks | Converse of the derived "Some bricks are boats" |
II | Some pens are bricks | Converse of the derived "Some bricks are pens" |
III | Some trees are bricks | Converse of the given "Some bricks are trees" |
IV | Some bricks are boats | Chained through both universal premises |
Since each of the four listed statements is reached this way, all four hold, and the correct choice is the one stating that all of them follow.