Answer first

Core relationship: A relation is transitive when two links can be chained through a shared item. Ordering, greater-than comparisons, and subset relationships are commonly transitive; adjacency and friendship are not.

For transitive relationships in ordering puzzles, begin with name the relation and finish with check whether equality is possible. The sequence keeps the starting facts, intermediate result, and final limit visible instead of relying on memory.

Build the analysis

Name the relation

Do not chain statements merely because they share a person or object. Capture the result before moving to keep direction consistent. A written output shows whether the next deduction follows from the evidence or quietly adds a new assumption.

Keep direction consistent

A before B and C before B do not determine A versus C. Compare this output with the warning about chaining adjacency. If that failure still fits, revise the representation before using the result in another deduction.

Compress confirmed chains

Write A before B before C so every implied pair remains visible. Use compress confirmed chains as a checkpoint. Name the input, the change made, and the conclusion that becomes available so another reader can reproduce the move.

Check whether equality is possible

Older than is strict; at least as old as may allow ties and changes the deductions. Finish by stating what this step establishes and what it leaves undecided. That boundary prevents a valid local conclusion from being stretched beyond the question.

Check against chaining adjacency

Questions for keep direction consistent

  • Can another reader reproduce name the relation from the stated information?
  • Did you complete keep direction consistent without reversing or enlarging the claim?
  • Does the result survive the failure mode chaining adjacency?
  • Which part remains uncertain after check whether equality is possible?

This check is specific to the method above. A clear answer should expose the evidence chain and the point where a different fact would produce a different conclusion.

Case note

Name the relation in the case

Rina finishes before Sol, and Sol finishes before Tariq, so Rina finishes before Tariq. If Rina sits beside Sol and Sol sits beside Tariq, Rina need not sit beside Tariq.

Why check whether equality is possible matters

The case starts with name the relation, then uses keep direction consistent to control the next inference. The conclusion is acceptable only after check whether equality is possible. Changing any fact that supports those moves can change the answer, while an unrelated detail should not.

Quality checks

Chaining adjacency

Next-to relationships usually fail transitivity. Return to name the relation and rebuild only from information the problem actually provides.

Reversing one link

A chain only works when the arrows align conceptually. Compare the disputed move with compress confirmed chains; the two should use the same definitions and direction.

Ignoring ties

Non-strict comparisons may not produce a unique order. Run the practice task while deliberately watching for ignoring ties. Record the first point where the reasoning begins to drift.

Apply it yourself

Sort ten relationship statements into transitive and non-transitive groups. For each transitive pair, state one additional conclusion it supports.

Continue after check whether equality is possible

Use the deductive reasoning hub for the broader method, then apply the idea in the truth table generator. Keep the written reasoning so the next attempt can improve a specific step rather than simply repeat the exercise.

Compare this method with Build an Elimination Table for Logic Puzzles, then continue to How to Solve Ordering Puzzles With Slots for a different reasoning task.