Help sought to solve ~(A&B) / ~(A&~B) // ~A

Question

A student contacted me asking for assistance in validating this symbolic logic (propositional) argument:

~(A&B)

~(A&~B)

~A

The question required the use of the Assumed Indirect Proof method, and required that it be solved in a certain number of steps.

Answer 1

We proceeded as follows. Lines in bold were premises or provided as part of the assignment:

1. ~(A&B)
2. ~(A&~B) / ~A
3. | A AIP
4. | | B AIP
5. | | A&B 3,4 Conjunction
6. | | (A&B) & ~(A&B) 1,5 Conjunction
7. | ~B 4, AIP Discharged
8. | A&~B 3,7 Conjunction
9. | (A&~B) & ~(A&~B) 2,8 Conjuction
10. ~A 3, AIP Discharged