Three statements are given, followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: No bench is chair. All sofas are benches. All tables are sofas. Conclusions: I. No table is a chair. II. Some sofas are chairs. III. All tables are benches.

Correct — C. Chain the two universals, then let the negative statement fall through the chain.

Rule: all tables are sofas, all sofas are benches, and no bench is a chair.

Conclusion III: all tables are sofas and all sofas are benches, so all tables are benches. It follows.

Conclusion I: tables sit inside benches, and no bench is a chair, so no table can be a chair. It follows.

Conclusion II: sofas also sit inside benches, so no sofa is a chair either. II is not merely unproven, it is ruled out.

I and III together is option (c).

Why the others are wrong

• (a)
  Only conclusion II follows — Option (a) picks the one conclusion the statements forbid. Sofas lie inside benches, and no bench is a chair, so no sofa is a chair.
• (b)
  Only conclusions I and II follow — Option (b) is right about conclusion I but keeps II. No bench is chair is a universal negative, and it is inherited by everything inside benches, sofas included.
• (d)
  Only conclusion I follows — Option (d) drops conclusion III, but all tables are sofas and all sofas are benches chain directly into all tables are benches.

Two rules settle almost every SSC syllogism, and both are needed here.

A chain of 'all' statements passes straight through: all A are B and all B are C give all A are C.

A universal negative is inherited downwards: if no B is C, then nothing inside B is C either, so every subset of B carries the same exclusion.

Benches are the pivot in this question. Sofas and tables both lie inside benches, so the ban on benches being chairs reaches both of them.

Key facts

• All A are B plus all B are C gives all A are C.
• If no B is C then nothing inside B is C, so every subset of B inherits the exclusion.
• Tables lie inside sofas, sofas lie inside benches, and benches are wholly outside chairs.
• Some sofas are chairs is impossible here, not merely unproven.

Common traps

• Marking conclusion II as 'may or may not follow' when the statements actually forbid it
• Missing conclusion III because table and bench never appear in the same statement
• Treating 'no bench is chair' as a fact about benches only and not about what lies inside them

No directly related past PYQ was found.