SOLUTION: 1. ~(K v F) 2. ~F ⊃ (K v C) 3. (G v C) ⊃ ~H /~(K v H)

Question 1178946: 1. ~(K v F)
2. ~F ⊃ (K v C)
3. (G v C) ⊃ ~H /~(K v H)

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's analyze this logical argument to determine its validity. We'll use a proof by deduction to see if we can derive ~(K v H) from the given premises.
**1. Premises:**
1. ~(K v F)
2. ~F ⊃ (K v C)
3. (G v C) ⊃ ~H
**2. Derivations:**
4. ~K • ~F (De Morgan's Law on premise 1)
5. ~F (Simplification on line 4)
6. K v C (Modus Ponens on lines 2 and 5)
7. ~K (Simplification on line 4)
8. C (Disjunctive Syllogism on lines 6 and 7)
9. G v C (Addition on line 8)
10. ~H (Modus Ponens on lines 3 and 9)
11. ~K • ~H (Conjunction on lines 7 and 10)
12. ~(K v H) (De Morgan's Law on line 11)
**Explanation of Steps:**
* **Step 4:** We applied De Morgan's Law to premise 1. De Morgan's Law states that ~(A v B) is equivalent to ~A • ~B.
* **Step 5:** We used simplification on line 4. If a conjunction (A • B) is true, then both A and B are true individually.
* **Step 6:** We used Modus Ponens on lines 2 and 5. Modus Ponens states that if (A ⊃ B) is true and A is true, then B is true.
* **Step 7:** We used simplification on line 4, just as in step 5.
* **Step 8:** We used Disjunctive Syllogism on lines 6 and 7. Disjunctive Syllogism states that if (A v B) is true and ~A is true, then B is true.
* **Step 9:** We used addition on line 8. If A is true, then (A v B) is also true, regardless of the truth value of B.
* **Step 10:** We used Modus Ponens on lines 3 and 9. Modus Ponens states that if (A ⊃ B) is true and A is true, then B is true.
* **Step 11:** We used conjunction on lines 7 and 10. If A and B are both true, then (A • B) is true.
* **Step 12:** We applied De Morgan's Law to line 11. De Morgan's Law states that ~A • ~B is equivalent to ~(A v B).
**Conclusion:**
We were able to derive ~(K v H) from the given premises. Therefore, the argument is **valid**.

RELATED QUESTIONS
1. ~(K v F) 2. ~F ⊃ (K v C) 3. (G v C) ⊃ ~H / ~(K v... (answered by Edwin McCravy)

please help me solve this: 1.(F v G) > (H & I) 2. I > K 3.~k.:... (answered by Edwin McCravy)

Solve the two step proofs below: 1. ~C 2. A > B 3. B > C / ~A 1. D > E 2. F > G (answered by Edwin McCravy)

1. (R v S) > (H & ~G) 2. (K v R) > (G v ~H) / ~R (answered by jim_thompson5910)

1.(N V O) ⊃ (C • D) 2.(D V K) ⊃ (P V ~C) 3.(P V G) ⊃ (N • D) ∴... (answered by math_tutor2020)

1. (I v K)>~L 2. (H v J) >I 3. ~K 4. H v K... (answered by jim_thompson5910)

1. (I v K) > ~L 2. (H v J) > I 3. ~K 4. H v K... (answered by jim_thompson5910)

1. ~H 2. H v K 3. L >H 4. ~(K.~L) v (~L.M) /... (answered by jim_thompson5910)

1. (F v S) > (V * G) 2. F * (C = D) / F *... (answered by jim_thompson5910)