SOLUTION: Use the quantifier negation rule together with the eighteen rules of inference to derive the conclusion of the following symbolized argument. Do not use either conditional proof or

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Question 1210174: Use the quantifier negation rule together with the eighteen rules of inference to derive the conclusion of the following symbolized argument. Do not use either conditional proof or indirect proof. (Complete the proof in the logic tool. See the Getting Started text for further instructions. Select the Submit button to grade your response.)
Step Argument Justification
1. ~(∃x)(Ax ⦁ ~Bx)
2. ~(∃x)(Ax ⦁ ~Cx) / (x)[Ax ⊃ (Bx ⦁ Cx)]
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
```
1. ~(∃x)(Ax ⦁ ~Bx) Premise
2. ~(∃x)(Ax ⦁ ~Cx) Premise
3. (x)~(Ax ⦁ ~Bx) QN 1
4. (x)~(Ax ⦁ ~Cx) QN 2
5. ~(Aa ⦁ ~Ba) UI 3
6. ~(Aa ⦁ ~Ca) UI 4
7. ~Aa ∨ ~~Ba DM 5
8. ~Aa ∨ Ba DN 7
9. ~Aa ∨ ~~Ca DM 6
10. ~Aa ∨ Ca DN 9
11. Aa ⊃ Ba Impl 8
12. Aa ⊃ Ca Impl 10
13. Aa ⊃ (Ba ⦁ Ca) Conj 11, 12
14. (x)[Ax ⊃ (Bx ⦁ Cx)] UG 13
```