B.5.QD:4.2 - Find the relation that can change the question
Follow the earlier result back to a consequential dependency, or forward to an operation it enables.
If a description gives the same information for cases that need different answers, construct two such cases. Their difference identifies information a stronger question may need. If an inference depends on an unproved step, state the missing step as a possible question. If an operation succeeds, ask which other inputs, outputs or combinations preserve its useful relation.
Use variations that have a reason in the work. The following are common ways to construct them.
| What the work reveals | How to form the next question |
|---|---|
| A counterexample identifies a failed condition. | Ask which condition would support the needed conclusion, or which construction identifies the cases where it fails. |
| A successful construction produces more information than the first answer used. | Ask what further result can be obtained from that information and by which operation. |
| Different cases collapse to one description. | Ask what additional distinction determines the answer, or what bound remains possible without it. |
| An argument needs an unavailable intermediate result. | Ask for a lemma, witness or construction that supplies that step; state how it would be used. |
| A familiar operation becomes available in another setting. | Ask whether its required relations hold there and what receiving task it can now serve. |
A variation can change the original task. Preserve that change explicitly: restricting a claim to trees may give a valid result while leaving the original request about all graphs unanswered. If the broader request still matters, keep it as an unresolved question.
These variations can be combined or repeated. Their purpose is to expose a useful answer, not to fill a catalogue of question types.
When requirements appear incompatible, B.5.QD.CF recovers the premises producing the conflict and asks what other construction could satisfy the retained need. It distinguishes changing an assumed means or representation from changing a requirement, and can return a useful impossibility when the conditions must remain.