Can someone explain the difference (Logically) of the following symbol set. \(\Leftrightarrow\) \(\equiv\) \(\leftrightarrow\) ¬ 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 \(A = B \, \, \Leftrightarrow \, \, A - B = 0\) would be a theorem (or axiom) connecting two sentences, while \(( ( A = B ) \leftrightarrow ( C \ne D ) ) \rightarrow ( (A - B)(C-D) = 0 )\) 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 :worship: you lost me at modus pones... :shrug:
