Art of Problem Solving

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'''Logic''' is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument.
'''Logic''' is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument. it is sometimes considered a branch of [[abstract algebra]].


==Logical Notation==
==Logical Notation==
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'''Logical notation''' is a special syntax that is shorthand for logical statements.
'''Logical notation''' is a special syntax that is shorthand for logical statements.


For example, both <math>p\to q</math> and <math>p \subset q</math> mean that p ''implies'' q, or  
For example, both <math>p\to q</math> and <math>p \subset q</math> mean that p ''implies'' q, or "If ''p'', then ''q''."
If ''p'', then ''q''.
Note that this can be also written <math>p \cup ~q</math>, or "''p'' or not ''q''".
==See Also==
*[[Dual]]
*[[Abstract algebra]]
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Revision as of 10:51, 23 November 2007

Logic is the systematic use of symbolic and mathematical techniques to determine the forms of valid deductive or inductive argument. it is sometimes considered a branch of abstract algebra.

Logical Notation

Main article: Logical notation

Logical notation is a special syntax that is shorthand for logical statements.

For example, both $p\to q$ and $p \subset q$ mean that p implies q, or "If p, then q." Note that this can be also written $p \cup ~q$, or "p or not q".

See Also

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