Can someone explain the difference (Logically) of the following symbol set.







¬

For example...what's the difference between the following statements...

A¬B and A→!B


Is it simple application differences?

and...

Is there just a symbol symbol for "If"
As in...
(IF) A^BvC --> D

The fourth symbol is not a symbol of equivalence, as I understand it - it is the NOT symbol for logical negation. Another symbol for NOT is !, so ¬A and !A both mean "NOT A".

The other three symbols are symbols of equivalence, which is the same as "if and only if".

There's no need for a symbol for "if", since a statement like

A -> B

already means "if A is true then B is true".

Right and thanks, my post was poorly divided into sections.

Regarding the first 3, is there no difference in functionality or better said...is there an instance where symbol 1 in a certain context is more valid and/or conventionally accepted than symbol 2?

I don't know of the third symbol. In typical mathematics I would say the first one is used to denote equivalence between sentences, and the second one is to denote identity between functions.

All language is contextual -- meaning various authors can define the symbols to mean something different than any reference tells you.

But, I have see the first being used as a true equivalences between sentences, and the third as a logical connective within a sentence.

So would be a theorem (or axiom) connecting two sentences, while would be a single sentence, of the form "if just one of A = B and C = D is true, then (A - B)(C-D) = 0." With a theorem (or axiom) in a single sentence, you need to construct a syllogism (using something like modus pones) to apply it.

we need more math geeks in the world..keep it up guys..lol

you lost me at modus pones...