by Fred J. Schaal

This lesson was created as a part of the SMART website and is hosted by the Illinois Institute of Technology

The **purpose** of this web page is to introduce some
fundamental Boolean
Algebra ideas.

These notions are pretty different, so suspend all judgment until you have mastered the basics. Take this stuff on faith. Look up Mr. < a href="http://www.kerryr.net/pioneers/boole.htm"> Boole on the internet for details of his fascinating life and times.

The Boolean operations that I shall deal with are **and**--L
and ** or**--V.
There are other symbols for these operations but they are to be
avoided.
(Confusion lies is their wake.)

I want to set up the** truth table** for ** truth table** for

A |
B |
ALB |
AVB |

T | T | T | T |

F | T | F | T |

T | F | F | T |

F | F | F | F |

The ** variables** in Boolean, here A and B, take only two
values. I use
T and F, standing for **true** and **false**, but others
use 1 and 0, red and green, on and off, in and out, etc.
The idea is to have two easily distinguishable values. Under A
I *blink* the variable thru its possible values: T, F, T,
F. Under B I * stutter blink*
the variable thru its
possible values: T, T, F, F. For the case of just two variables
there are just
four cases to handle all possible combinations of the values of the
variables: T
T, F T, T F, F F. Think about this!.

Knock, Knock.

Who's there?

Boo.

Boo who?

BOO BOO BOOLEAN!

T and T is T
but all the
rest are F. T or T
is T and only F or
F is F.
L
likes to be F. Therefore any F will make
L
F. V
likes to be T and any T will make it T. The only time
that

A third thing I need is negation. Not
A and Not B.
Some
people use the tilde before the variable to indicate negation ~A,
but I prefer to
use a bar over the variable to indicate negation. e.g.
A¯.
Unfortunately
I cannot get the bar to appear *over * the variable.
So I shall be content to
have it *lag a snidge* behind the negated variable.
Below is a table
of two variables and their
negations:

A |
B |
A¯ | B¯ |

T | T | F | F |

F | T | T | F |

T | F | F | T |

F | F | T | T |

Now * *I shall create the opportunity for you to and
and to or
a variable with
its negation.

A | A¯ | ALA¯ | AVA¯ |

T | F | ||

F | T |

To do these fill ins just look at the table for and and or. Recall that and likes to be false and or likes to be true.

How about doing A and B¯
and A¯
or B?
I'll even let
you fill in the columns for B and the negated variables not
A and not B.
Refer to the
above truth table for negation and to the previous truth table for and
and or.
Be sure to *stutter
blink *

A | B | A¯ | B¯ | ALB¯ | A¯VB |

T | |||||

F | |||||

T | |||||

F |

Print these pages and fill in the missing entries in the above tables. Highlight the important ideas is the text. Use the approved color scheme for these highlights. Return these pages to me in a sealed envelope. Put my name, your name and period, the date, and the name of this web page on the envelope.

Once you have filled in the tables you may cheer

in the words of George W....

BOOLA BOOLA, BOOLA BOOLA etc.

An after thought about the color coding used on this web page: AND is yellow, OR is cyan, NOT A is red and NOT B is green.

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