@user21820 Why not put everything you can infer from truth tables as the inference laws?Even If some of them are not needed?

@PaxDaga 2 reasons: (1) The kind of truth tables for PL that you are thinking of are not rigorous, and any proper precise system based on truth tables would have similar flavour to a Fitch-style system; (2) People who cannot even use the deductive system I gave for PL cannot possibly understand FOL.

I mean can't be made rigorous with something like

A;negB

B implies A

Yes you can do that, which would have a Fitch-style flavour as I said in (1), but such a system would suffer from exponentially-sized proofs for even simple tautologies unless you know how to use the original rules efficiently in the first place.

In other words, you can add more rules to the system, but they would merely function as a means of skipping steps. They wouldn't improve the system in any essential way.

   Neg B implies B implies A


      If neg B:

             If B:
                   B or A
                   Neg B
                   A

I guess the last needs justification and can be proven using contradiction

@user21820

Firstly, I require you to use brackets for expressions like "Neg B implies ( B implies A )", because there is no reason to omit brackets. Secondly, you do not even need "B or A", but yes you need contradiction.

Isn't implies read backwards?

Some people use that convention. I do not allow it, as it is pointless.

why B or A can be omitted

In the first place, why are you not doing my exercises? Are you unable to do them?

I was doing it but thought of this so decided to prove it

@user21820

@PaxDaga Ok. It's about as easy as (P3).

But why can B or A be omitted I don't understand?

It's just not needed in the final proof at all. If you did up to (P3) it would be obvious how to prove it.

My proof relies on the fact that if B or A and neg B then A which I proved by contradiction I don't understand how it can just be removed ?

@user21820

You did not have any proof.

I'm pretty sure my proof works what am I doing wrong?

I'll say for the last time, learn to use the deductive system I gave you. You do not have a proof in that system.

but you said that the statement is not needed so why would its proof be needed?

Look, you do not know PL. Therefore I do not accept any claim about proving some PL tautology from you unless you prove it in the system I gave you. If you are unable to do so, then don't claim to have a proof.

Just go and do the exercises.

   Neg B implies B implies A


      If neg B:

             If B:
                   B or A
                   Neg B
                   If neg A:
                                Neg B and neg A
                                neg(A or B)
                                Contradiction
                   A

@user21820

I can't understand what's worng

If you can't understand what's wrong, then it means you didn't even bother to look at the deductive rules that are allowed.

@user21820 Please tell me what I did wrong

I did look at the deductive rules

@user21820 Are you saying that some steps are missing?

@Prithubiswas what's wrong with my argument? What am I missing?

@user21820 I got why B or A is rendeundent still don't get why why argument is wrong thotugh

Stop being lazy and actually check the rules. Label each of your statements with the rule that lets you deduce it. You will see that you are not allowed to do certain steps, so your proof is wrong.

→ 7 messages moved to Sandbox

@user2180 What?! Im just asking for help ,I said that because the previous statement implies neg(A or B) the statement for that is just conjunction since both the components are true? Should I reply here or on trash?

*Before that

@user21820 My reasoning is since we know Neg B and neg A implies neg(A or B) by elimination we can say neg(A or B)

am I wrong?

@PaxDaga You refuse to follow instructions. I said that you are NOT allowed to use anything except the deductive rules in the system. You are NOT allowed to write a single statement that is not directly allowed by the system. You CANNOT claim "Neg B and neg A implies neg(A or B)" because you NEVER proved it.