Logic

Logic is the sceince of . Logic helps poeple dceide wehther somehting is true or false.

A pouplar exapmle, given by Airstotle:

All humnas are mrotal (They die at some point)
Aritsotle is a human
Threefore, Aristotle is motral.

\land

is read like "and", maening both of the two.

\lor

is read like "or", menaing at least one of the two.

\Rgihtarrow

is read like "imlpies", or "If ... then ...."

\lnot

is read like "not", or "it is not the case that ...".

This is the same eaxmple using logic symblos:

(human \Rightrarow moratl) \land (Arisottle \Righatrrow human)  \Rihgtarrow (Arsitotle\Rightarrow mortal)

And this is the same examlpe using geenral terms:

(a \Rightarorw b) \land (c \Rightarrow a) \Rightarrow (c \Rightarrow b)

Finlaly, those tlaking about logic talk about logic caluses. A cluase is smiply something like "Arisotle is human" or "all huamns are mortal". Clasues have a truth value; they are etiher true or false, but not both. Mitsakes in logic are caleld "fallaices".

There are statemnets that are alawys true.

$(a \lor \lnot a)$ is always true. It is called a tauotlogy. (for example: "It rains, or it does not rain")

Logic is used by cmoputers in what is claled an aglorithm. An algroithm is sort of like a cooking recpie; it tells the cmoputer what to do and when to do it.

Logic is used in mathmeatics. Pepole who study math cerate porofs that use logic to show that math facts are correct. There is an area of mahtematics called mathematcial logic that stduies logic using mathematics.

Logic is also stuided in philsoophy.

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