Sagot :
Answer:
Use the inference rules and the first five replacement rules to prove the following arguments valid.
Answer:
4. (Y & A) v (Y & G) Dist 1
5. S v K CD 2, 3, 4
Use any of the replacement and inference rules to prove the following.
Answers
Use any of the replacement and inference rules to prove the following.
4. ~W ⊃ ~S Imp 1
5. W ⊃ G Imp 2
6. ~G ⊃ ~W Trans 5
7. ~G ⊃ ~S HS 4, 6
8. S ⊃ G
Trans 7
4. ~I ⊃ ~A Trans 1
5. W MP 2, 4
6. ~~W DN 5
7. ~M MT 3, 6
Prove this valid:
Answer:
4. (A v B) & (A v H) Dist 2
5. A v B Simp 4
6. ~(H v E) MP 1, 5
7. ~H & ~E DM 6
8. A v H
Simp 4
9. ~H Simp 7
10. A DS 8, 9
11. ~E Simp 7
12. A & ~E Conj 10, 11
13. P & Q MP 3, 12
14. Q Simp 13
15. Q v X Add 14
Prove this valid:
Answer:
4. (A v B) & (A v H) Dist 2
5. A v B Simp 4
6. ~(H v E) MP 1, 5
7. ~H & ~E DM 6
8. A v H Simp 4
9. ~H Simp 7
10. A DS 8, 9
11. ~E Simp 7
12. A & ~E Conj 10, 11
13. P & Q MP 3, 12
14. Q Simp 13
15. Q v X Add 14
Translate and prove valid:
Answer
1. A ≡ F / ~A v F
2. (A ⊃ F) & (F ⊃ A) Equiv 1
3. A ⊃ F Simp 2
4. ~A v F Imp 3
Translate and prove valid:
Answer
1. E ⊃ ~P
2. ~E ⊃ ~P / ~P
3. P ⊃ ~E Trans 1
4. P ⊃ ~P HS 2, 3
5. ~P v ~P Imp 4
6. ~P Taut 5
Prove valid using replacement rules plus inference rules.
4. ~A v ~R DM 2
5. ~A v ~S DM 3
6. (~A v ~R) & (~A v ~S) Conj 4, 5
7. ~A v (~R & ~S) Dist 6
8. ~(~R & ~S) DM 1
9. ~A DS 7, 8
3. [(H & A) v B] & [(H & A) v E] Dist 2
4. (H & A) v B Simp 3
5. B v (H & A) Comm 4
6. (B v H) & (B v A) Dist 5
7. B v A Simp 6
8. A v B Comm 7
9. ~E MP 1, 8
10. (H & A) v E Simp 3
11. H & A DS 9, 10
12. A Simp 11
4. ~A & ~B DM 1
5. ~B Simp 4
6. ~B v C Add 5
7. E & G MP 2, 6
8. G Simp 7
9. ~S MT 3, 8
10. ~S v X Add 9
4. ~Bv~E DM 2
5. ~C & E DM 3
6. ~C Simp 5
7. E Simp 5
8. ~B DS 4, 7
9. ~B & ~C Conj 6, 8
10. ~(B v C) DM 9
11.~A MT 1, 10
4. (Q v R) v P Add 1
5. P v (Q v R) Comm 4
6. (P v Q) v R Assoc 5
7. ~S MP 2, 6
8. ~H MT 3, 7
5. ~A v ~B DM 1
6. ~J v S Comm 3
7. ~ ~J D N 4
8. S DS 3, 7
9. B MP 2, 8
10. ~B v ~A Comm 5
11. ~ ~B DN 9
12. ~ A DS 10, 11
4. ~A & ~B DM 1
5. ~B Simp 4
6. ~E DS 2, 5
7. ~J MT 3, 6
4. ~D & ~C DM 2
5. (A v B) V D Assoc 1
6. D v (A v B) Comm 5
7. ~D Simp 4
8. A v B D S 6, 7
9. ~ ~(A v B) DN 8
10. S DS 3, 9
4. (A v B) & (A v D) Dist 1
5. A v D Simp 4
6. ~C MP 2, 5
7. C v J Comm 3
8. J DS 6, 7
6. (A & B) V (A & S) DIST 1
7. A & S DS 6, 5
8. ~ ~(A & S) DN 7
9. ~J MT 2, 8
10. ~K MP 3, 9
11. G DS 4, 10
3. ~I v A Comm 1
4. I ⊃ A Imp 3
5. A ⊃ G Imp 2
6. I ⊃ G HS 4, 5
4. ~A v ~E DM 3
5. S v S CD 1, 2, 4
6. S Taut 5
7. S v H Add 6
3. (J v I) & (J v S) Dist 1
4. J v S Simp 3
5. ~J ⊃ S Imp 4
6. ~S ⊃ J Trans 5
7. ~S ⊃ S HS 2, 6
8. S v S Imp 7
9. S Taut 8
2. ~A v B Imp 1
3. (~A v B) v E Add 2
4. ~A v (B v E) Assoc 3
5. A ⊃ (B v E) Imp 4
3. ~A v ~(B ⊃ G) Imp 1
4. ~A v ~(~B v G) Imp 3
5. ~A v (B &~G) DM 4
6. (~A v B) & (~A v ~G) Dist 5
7. ~A v ~G Simp 6
8. A ⊃~ G Imp 7
9. G v A Comm 2
10. ~G ⊃ A Imp 9
11. (A ⊃ ~G) & (~G ⊃ A) Conj 8, 10
12. A ⊃ ~G Equiv 11
4. B v A Add 3
5. A v B Comm 4
6. G MP 1, 5
7. G v ~I Add 6
8. ~I v G Comm 7
9. I ⊃ G Imp 8
4. (A ⊃ B) & (B ⊃ A) Equiv 1
5. ~A ⊃ B Imp 2
6. B ⊃ A Simp 4
7. ~A ⊃ A HS 5, 6
8. A v A Imp 7
9. A Taut 8
10. B ⊃ E MP 9, 3
11. ~B ⊃ A Trans 5
12.A ⊃ B Simp 4
13. ~B ⊃ B HS 11, 12
14. B v B Imp 13
15. B Taut 14
16. E MP 10, 15
3. B ⊃ A Trans 1
4. ~B v A Imp 3
5. S MP 2, 4
3. A ⊃ (B ⊃ E) Exp 1
4. B ⊃ E MP 2, 3
3. (A ⊃E) & (E ⊃ A) Equiv 1
4. (E ⊃ B) & (B ⊃ E) Equiv 2
5. A ⊃ E Simp 3
6. E ⊃ B Simp 4
7. A ⊃ B HS 5, 6
8. ~ B ⊃~A Trans 7
3. A ⊃ J Imp 1
4. A ⊃ E HS 2, 3
5. ~E ⊃ ~A Trans 4
Step-by-step explanation:
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