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- Show validity using resolution:
- Premises:
- (note: v = or, ^ = and)
- 1. ~q v s
- 2. ~(s ^ p)
- 3. (p -> q) ^ r
- 4. p -> r -> p
- therefore: ~(s -> p)
- Derivation:
- 5. ~s v ~p 2 DeMorgans
- 6. ~p v ~q 1, 5 res
- 7. p -> q from 3
- 8. ~p v q from 7
- 9. r from 3
- 10. ~p v ~p 6, 8 res
- 11. ~p from 10
- 12. p -> r -> p <=> ~(~p v r) v p <=> (p ^ ~r) v p
- 13. p ^ ~r from 11 and 12
- 14. p from 13
- 15. ~r from 13
- Contradictions between lines 15 and 9, 14 and 11.
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