what is mathematical logic?
Logic is the science of formal principles of reasoning or correct inference. Logic originated from the Greek philosopher Aristotle. According to him, reasoning is any argument in which certain assumptions are laid down and then something other then these necessarily follows. Therefore logic is the science of necessary inference.
Logic does not really concern itself with whether the propositions are actually true or false - only the reasoning leading from one proposition to the next.
Logic does not really concern itself with whether the propositions are actually true or false - only the reasoning leading from one proposition to the next.
basics of symbolic logic
Propositions - The building block of logic is the proposition. This is a statement that can have one of two values, true or false. "I paint pictures" and "x > 4" are propositions, whereas "What is the time?" and "2x - 3" are not. Propositions can be represented by a small letter.
e.g.: p: x > 4 reads as "p is the proposition that x > 4"
Negation - The negation of a proposition is formed by putting in words such as "not" or "do not". Its symbol is ¬.
e.g.: p: "I paint pictures" ¬p: "I do not paint pictures"
p:"x > 4" ¬p: x < 4
Note that negation is not the same as "opposite". For example:
p: "The glass is full" ¬p: "The glass is not full
You could not use "The glass is empty" because if the glass is not full, it could still have some water in it.
e.g.: p: x > 4 reads as "p is the proposition that x > 4"
Negation - The negation of a proposition is formed by putting in words such as "not" or "do not". Its symbol is ¬.
e.g.: p: "I paint pictures" ¬p: "I do not paint pictures"
p:"x > 4" ¬p: x < 4
Note that negation is not the same as "opposite". For example:
p: "The glass is full" ¬p: "The glass is not full
You could not use "The glass is empty" because if the glass is not full, it could still have some water in it.