An if–then statement gives a one-way relationship unless the problem adds another rule. Understanding that direction prevents two of the most common errors in logical reasoning.
Start with the rule
If a card is gold, it opens the door. Let G mean gold and O mean opens the door. The rule is G → O.
A gold card must open the door under the stated rule. A card that does not open the door cannot be gold. The second inference is the contrapositive: not O → not G.
What does not follow
If a card opens the door, it need not be gold. A silver card might also open it. Concluding gold from opens reverses the implication.
If a card is not gold, it does not follow that it fails to open the door. The rule said what gold cards do, not what every other card does.
| Gold? | Opens? | Compatible with the rule? |
|---|---|---|
| Yes | Yes | Yes |
| Yes | No | No |
| No | Yes | Yes |
| No | No | Yes |
Watch for an added reverse rule
If the problem also states that only gold cards open the door, you now have O → G as well. Together, the two rules establish equivalence in this example. Do not silently add that second rule when it is absent.
Practice the direction
All sealed parcels have a label. A parcel has no label. Can it be sealed under the rule? No. If it were sealed, it would have a label, contradicting the observation.
A parcel with a label, however, is not necessarily sealed. Give yourself a moment to distinguish these two cases. The same conditional structure appears in invented-symbol questions, everyday arguments and multistep logic puzzles, even when the wording changes.