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Put the following statements into order to prove that the modus ponens is a valid argument form. Not all steps are correct or belong in the proof. Enter N for such steps.
1. Since the disjunction of an expression and its negation is always true, is a tautology. This completes the proof.
2. By the domination law, the last expression is always true. This completes the proof.
3. Using the rule , we rewrite the given expression as
4. To prove the validity of the modus ponens, we need to show that is a tautology.
5.
6. To prove the validity of the modus ponens, we need to show that is a tautology.
7.
8. We now use one of the rules of De Morgan:
9.
10.
11. We now reorder and re-associate the terms of the last expression by using the associative and commutative laws and apply the rule again:
12.
13. Using the rule , we rewrite the given expression as
14.

Respuesta :

adioabiola

The prove that the modus ponens is a valid argument form in correct order is

  • To prove the validity of the modus ponens, we need to show that (p 5 9) 5 4 is a tautology:

  • Using the rule p 4 q =7p ^ q, we rewrite the given expression as 13

  • Zp V-(p - 9) Vq = (~p V 9) ^ -(-p V9)

  • ~(p ^ (p + 9)) Vq =-pV (p + 9) Vq 10

  • (p v q) - 4=-pv 9Vq

  • We now use one of the rules of De Morgan

  • By the domination law; the last expression is always true: This completes the proof

  • Using the rule p 7 q =7p V 4, we rewrite the given expression as 12

How to prove modus ponens

The complete question is given below:

1. ~p V -(p = q) Vq = (Tp Vq) v-(Tp V q)

2. Since the disjunction of an expression and its negation is always true, Zp V q) v-(-p V q) is a tautology: This completes the proof:

3. ~(p ^ (p + 9)) Vq =-pV (p + 9) Vq 10

4. Using the rule p 7 q =7p V 4, we rewrite the given expression as 12

5. ~(p ^ (p = 4) Vq =-pv-Wpv 9)Vq

6. To prove the validity of the modus ponens, we need to show that (p 5 9) 5 4 is a tautology:

7. We now reorder and re-associate the terms of the last expression by using the associative and commutative laws and apply the rule p v q = 7pV q again: N

8. To prove the validity of the modus ponens; we need to show that (p ^ (p 7 74 is a tautology:

9. (p v q) - 4=-pv 9Vq

10. Using the rule p 4 q =7p ^ q, we rewrite the given expression as 13

11. By the domination law; the last expression is always true: This completes the proof: 11

12 Zp V-(p - 9) Vq = (~p V 9) ^ -(-p V9)

13. We now use one of the rules of De Morgan:

14. (p ^ (p = 9)) - q =-(p ^ (p = 9)) V q

Learn more about proofing:

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