Proof Question

Tags:
1. Dec 6, 2014

Jennifer_T

1. The problem statement, all variables and given/known data
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).

2. Dec 6, 2014

Joffan

please explain your point 5). It's wrong, but I want to know what your reasoning was.

3. Dec 6, 2014

Jennifer_T

I actually see my mistake. I was thinking of Law of Excluded Middle, but that actually states x or not x which means that my point was wrong.