60. Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the following
conclusions can be deduced from the preceding sentences?
(i). At least one bench is a table
(ii). At least one shelf is a bench
(iii) At least one chair is a table
(iv) All benches are chairs
(a) Only (i) (b) Only (ii)
(c) Only (ii) and (iii) (d) Only (iv)

Logical Analysis of the Syllogism

This is a classic syllogism problem in logical reasoning, testing deductions from categorical statements. The premises are:

1. Some tables are shelves. (Some T → S)

2. Some shelves are chairs. (Some S → C)

3. All chairs are benches. (All C → B)

We need to determine which conclusions logically follow using Venn diagrams or distribution rules (no “all” statements reverse, “some” doesn’t imply “all,” etc.). “At least one” means some overlap exists.

Evaluating Each Option

• (i) At least one bench is a table
  No direct link between tables and benches. Tables overlap with shelves, shelves with chairs, and chairs with benches, but “some-some-all” chains don’t guarantee table-bench overlap. Possible that table-shelf area avoids chairs/benches entirely. Does not follow.

• (ii) At least one shelf is a bench
  Shelves overlap with chairs (some S → C), and all chairs are benches (C → B), so that shelf-chair overlap must be benches. Thus, some shelves are benches. Follows.

• (iii) At least one chair is a table
  Tables overlap with shelves, shelves with chairs, but no guaranteed table-chair overlap. The “some” links can miss each other (e.g., different shelf subsets). Does not follow.

• (iv) All benches are chairs
  Contradicts “all chairs are benches”—benches could include non-chairs. No premise forces this reverse. Does not follow.

Correct Answer: (b) Only (ii)

Visualize with Venn: Shelf circle overlaps table (partial) and chair (partial); chair fully inside bench. Shelf-chair overlap ⊂ bench, confirming (ii).

In competitive exams like SSC CGL, Bank PO, UPSC, and logical reasoning sections, syllogism questions like “some tables are shelves some shelves are chairs all chairs are benches” test your deduction skills. These puzzles ask which conclusions can be deduced from given statements, such as “at least one bench is a table” or “at least one shelf is a bench.” Mastering them boosts your score—let’s break down this exact question step-by-step.

Understanding Syllogism Basics

Syllogisms use categorical statements: “all,” “some,” “no,” or “some not.” Here:

• Some tables are shelves (partial overlap: T ∩ S ≠ ∅)

• Some shelves are chairs (S ∩ C ≠ ∅)

• All chairs are benches (C ⊂ B)

Key rule: Conclusions must hold in all possible diagrams (no assumptions beyond premises).

Step-by-Step Solution

Draw overlapping circles for tables (T), shelves (S), chairs (C), benches (B).

1. Premise 1: Shade T-S overlap.

2. Premise 2: Shade S-C overlap (separate from T-S possible).

3. Premise 3: Place all C inside B.

Now test options:

Answer: (b) Only (ii)—matches exams like “some tables are shelves some shelves are chairs all chairs are benches.”

Common Mistakes to Avoid

• Assuming “some-some” chains fully connect (e.g., T to B)—they don’t.

• Reversing “all” (all C → B ≠ all B → C).

• Ignoring “at least one” as existential quantifier.

Tips for Syllogism Success

• Use Venn diagrams for “some” statements.

• Apply distribution: Particulars (some) don’t distribute subjects.

• Practice 50+ questions daily from R.S. Aggarwal or Arihant books.

Nail “some tables are shelves some shelves are chairs all chairs are benches” and similar—perfect for reasoning prep!