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Complete the formal proof of this argument: 1. ~(A&B) 2. ~(A&~B) Thus, Remember: justify subproof assumptions with Assume; always drop outer parentheses; no spaces in PROP. 1. ~(A&B) 2. 3.1 4.|| 2. ~A 5. || 6.|| 7.1 8. | A&~B 9.1 10. Premise Premise ▬▬▬▬

Complete the formal proof of this argument: 1. ~(A&B) 2. ~(A&~B) Thus, Remember: justify subproof assumptions with Assume; always drop outer parentheses; no spaces in PROP. 1. ~(A&B) 2. 3.1 4.|| 2. ~A 5. || 6.|| 7.1 8. | A&~B 9.1 10. Premise Premise ▬▬▬▬

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Complete the formal proof of this argument: 1. ~(A&B) 2. ~(A&~B) Thus, Remember: justify subproof assumptions with Assume; always drop outer parentheses; no spaces in PROP. 1. ~(A&B) 2. 3.1 4.|| 2. ~A 5. || 6.|| 7.1 8. | A&~B 9.1 10. Premise Premise ILL
Transcribed Image Text:Complete the formal proof of this argument: 1. ~(A&B) 2. ~(A&~B) Thus, Remember: justify subproof assumptions with Assume; always drop outer parentheses; no spaces in PROP. 1. ~(A&B) 2. 3.1 4.|| 2. ~A 5. || 6.|| 7.1 8. | A&~B 9.1 10. Premise Premise ILL
Expert Solution
Step 1

Answer:

1.~(A&B)                       Premise

2.~(A&~B)                     Premise

3. I~~A          Assumption for indirect derivation

4.II A                          3,Double negation

5.II~Av~B                1,DeMorgan's Law

6.IIA-->~B                5,logical equivalence

7. I~ B                      Modus ponens,4,6

8. IA&~B                  Addition , 4,7

9. I~(A&~B)              Repeat ,2(contradiction)

10.  ~A                     Indirect derivation 3,9   

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