Analyzing Logical Arguments: Not A, B or Not C, B→ (A and D), E→(C)

[Jennifer_T]

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).

 

[Joffan]

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

 

[Jennifer_T]

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

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.