- 2071 Bhadra · 8 marks
Resolution: Sita and her umbrella
Short answer
Let r: raining, u: umbrella, w: wet. Clauses: ¬r ∨ u, ¬u ∨ ¬w, r ∨ ¬w, and w (negation of ¬w). Resolve r ∨ ¬w with w to get r; with ¬r ∨ u yields u; with ¬u ∨ ¬w yields ¬w; resolve with w yields □, proving Sita does not get wet.
Use resolution to show the hypothesis "It is not raining or Sita has her umbrella," "Sita does not have her umbrella or she does not get wet," and "It is raining or Sita does not get wet" imply that "Sita does not get wet."
Propositions
- r: it is raining
- u: Sita has her umbrella
- w: Sita gets wet
Hypotheses (already clauses)
- ¬r ∨ u
- ¬u ∨ ¬w
- r ∨ ¬w
Conclusion: ¬w. Its negation, w, is added as clause 4.
Resolution steps
| Step | Resolvent | From | Resolved on |
|---|---|---|---|
| 5 | r | 3, 4 | w |
| 6 | u | 1, 5 | r |
| 7 | ¬w | 2, 6 | u |
| 8 | □ (empty clause) | 4, 7 | w |
The empty clause is obtained, so the hypotheses together with w are unsatisfiable. Hence the hypotheses imply ¬w: Sita does not get wet. ∎
✓ Answer checked by Claude Opus 5.5 (high effort)
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