My proof for de morgans law

[LogicMaster]

It looks more readable for sure, but this is a very strange way to prove anything, i've never encountered such a way for a proof,and thus I can not say whether it is correct or not .

The simplest way to prove something is the truth table(the last 2 columns), but if you wanna do it the formal way, here is how ...
A longer but more understandable proof

Question to you ,Logicmaster : How many members do you think in this forum that have experience in these mathematical notations and how many of them studied Logic and Boolean algebra ? and if they did study that, how many of them still remember ?

Yeh, It's sometimes weird, but these types of proofs are called natural deduction proofs, It's how mathematics works, If you start with a true premise, then you deduce another from that, and on and on, until you get what you want to prove. It's simply mathematics and reason in disguise, Here:

Natural Deduction

And look, I can't tell how many people in this forum have experience because you have to be specialized in some subject in mathematics. I mean some universities include these subjects in there programs but not all. But the most common is Boolean algebra as you said, but the problem with Boolean algebra is that it only gives you equivalent forms, it doesn't give you the choice to "Infer" and "Deduce".

And again as you said why not "Truth Tables", the problem with truth tables is that it only can tell you if the statement is true or false, but again not inferences. But i am with you if you want to prove it with "Truth Tables", It's sufficient.

If you liked it and you want to read more here this book can teach you this way of reason:

Mathematical Logic

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Yeh, I'm really sorry about that here:

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Too big, for me.... you should have gone with imgfit tags

First I don't have a logical religiosity, I build up my thoughts through mathematics.

It's not that easy to tell what is really a true or false premise, the problem is that we really use logic to deduce true premises from other true premises though we will end up in the beginning with axioms.

The major problem with axioms is that it is hard to tell if a system of axioms is consistent or not, that means if our system is inconsistent then our axioms will make us deduce contradictions.

If you look at the progress in mathematics today, you will see "Open Problems", They are simply hypothesis and conjectures that no one ever found a proof for them from the mathematical system of axioms. Sometimes a genius mathematician simply changes some axioms and could prove the hypothesis, but it's not that easy.

But there are more problems, there are true premises that can't be proved and they are not axioms, by Godel's incompleteness theorems. So that's why we say "Existence" of mathematical facts.

So I wish you got my point.

I got your point: your religiosity (or religious thoughts) is built through [some form of] mathematics.... the axioms of which cannot be proven to be wrong, so you go with them.
(correct me if I was wrong there!)

No you are wrong once again, I know what you are up to, you think that i have some thoughts that "God" is an "axiom", no that is not what i meant. And no "God" is not an "axiom" that can't be proven to be "Wrong" or "False".

Look I only mean that i think in the "Mathematical Way" which is the super set for logic (As i said in the first place). And i will still say it over and over again, my thought aren't "religious".

Simply the way i think, is the way any mathematician thinks, That's All.