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.

  1. A.

    Only I and II follow

  2. B.

    Only III and IV follow

  3. C.

    None follows

  4. 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:

  1. Start from the given premise: Some bricks are trees.

  2. Combine it with All trees are pens (shared term: trees) to get: Some bricks are pens.

  3. Combine Some bricks are pens with All pens are boats (shared term: pens) to get: Some bricks are boats.

  4. 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.

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