Question about Logic Proof

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Using the 10 Rules of Inference and the 9 Rules of Replacement I need to complete the following proof in 9 steps.

I could use a little help. Thanks in advance

[Nine steps]
1. C
2. (C & T) > ~T
3. (C & ~T) > T / T < > ~T
4.
5.
6.
7.
8.
9. T < > ~T

"<>" means "if and only if"

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Re: Question about Logic Proof

maporsche wrote:

Using the 10 Rules of Inference and the 9 Rules of Replacement I need to complete the following proof in 9 steps.

I could use a little help. Thanks in advance

[Nine steps]
1. C
2. (C & T) > ~T
3. (C & ~T) > T / T < > ~T
4.
5.
6.
7.
8.
9. T < > ~T

"<>" means "if and only if"

I'm not sure I understand your notational system, but are you trying to prove "T" if and only if "not T?" If so, you're trying to prove a contradiction, aren't you?

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Yeah, I guess I'm trying to prove out a contridiction. Here is what I came up with. I haven't received feedback from my instructor yet. We'll see what he says.

Code:



1. C 

2. (C & T) > ~T 

3. (C & ~T) > T            /  T < > ~T

4. C > (T > ~T)		      (2) Exp.

5. C > (~T > T)		      (3) Exp.

6. T > ~T			         (4)(1) M.P.

7. ~T > T			         (5)(1) M.P.

8. (T > ~T) & (~T > T)	  (6)(7) Conj.

9. T <> ~T			        (8) Equiv.

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maporsche wrote:

Yeah, I guess I'm trying to prove out a contridiction.

Well then you're doing something wrong. It looks to me like your premise at step 2 is itself a contradiction. I suppose if you start with a contradictory premise you can arrive at a contradictory conclusion, but it doesn't make much sense.

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