Given The Following 2 Premises, 1. 𝑝→(𝑞∨𝑟) 2. 𝑞→𝑠 Prove 𝑝→(𝑟∨𝑠) Is Valid Using The Proof By Contradiction Method. [Hint: Use A Combination Of Equivalence Laws And Rules Of Inference To Solve This Question]
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Proof by Contradiction Method:
- Premise
- Premise
- Premise, proof by contradiction
- 3, Definition of
- 4, DeMorgan’s law
- 5, Specialization
- 5, Specialization
- 7, DeMorgan’s law
- 8, Specialization
- 8, Specialization
- 2, 10, Modus Tollens
- 9, 11
- 12, DeMorgan’s law
- 1, 13, Modus Tollens
- False 6, 14, proof by contradiction
Premise was false, so must be true.