Math Project

Boolean Logic

Invented by George Boole who developed an entire aspect of algebra on this topic, boolean logic is a simple and systematic way of thinking and reasoning.  In mathematics and philosophy, boolean logic can be applied to assess the validity of a mathematical expression or a sentence.  Let's start with a set of statements followed by a "true" if the statement is valid and "false" it is invalid.

1. Apples are red--true.

2. Violets are blue--true.

3. Three plus three is equal to seven--false.

If the statements were linked together with "AND" or "OR" or negate the statement with "NOT"  in combinations of pairs, then the validity of the entire sentence can be established based on the validity of the sub-statements.   Thus,

Statement | Basic Elements | Final Value |

Apples are red AND violets are blue. | True AND True | True |

Apples are red AND Three plus three is equal to seven. | True AND False | False |

Apples are red Or Three plus three is equal to seven. | True OR False | True |

Apples are red OR Violets are blue. | True Or True | True |

NOT Apples are red(i.e. Apples are not red.) AND violets are blue. | False AND True | False |

...etc... | ...etc... | ...etc... |

The combinations are not limited to pairs of statements linked by "AND" or "OR."  A sentence can have an unlimited number of statements all linked together by "AND" or "OR", but only two comparisons can be done at a time, so the statements are nested into parentheses(like in math where the statement in the innermost parentheses are evaluated first):

(Apples are red OR violets are blue) AND three plus three is equal to seven.  | (True OR True) AND False = (True) AND False = True AND False | False |

The combination of statements allowed a sentences or a mathematical expressions to clearly express their meanings simplistically yet be powerful and effective.  Thus, this was an attempt to formalize thought and reasoning at the mathematics level.

Computer...