- #1
Jennifer_T
- 8
- 0
Homework Statement
Hypotheses: not a, b or not c, b→ (a and d), e→(c)
Conclusion: not e
2. The attempt at a solution:
So far, I have this: 1) not a as premise
2) b or not c as premise
3) b→ (a and d) as premise
4) e→(c) as premise
5) a by Step 1 and Law of Excluded Middle.
6) c is true by Step 5 and 4 a and e→c and Modus Ponens.
7) c→b is true by Step 2 and implication.
8) b→a and b→d by Step 3.
I am unsure of what my next step(s) should be. I feel that it may be ((e implies c) and not c) implies not e) (Modus Tollens). I maybe should have 9) not c by Step 6 and Law of Excluded Middle. And then 10) ((e implies c) and not c) implies not e) (Modus Tollens).