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Truth Tables: a AND b

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Date: 09/10/2001 at 22:43:08
From: Emilee Longfellow
Subject: Truth Tables

I am having trouble finding out what truth tables are.

Emilee
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Date: 09/11/2001 at 03:36:36
From: Doctor Jeremiah
Subject: Re: Truth Tables

Hi Emilee:

Truth tables are a way of showing the answer to a question by listing
every possible value of every input and giving each the correct

For example let's take the operation called "and."

When you say "when a is true AND b is true ..."
what do you mean?

What do you mean when b is not true and a is true?
What do you mean when neither one is true?

To show what the answer is for every possible value
of a and b we need to make a truth table:

a   |   b   |  a AND b
------+-------+----------
false | false |
false | true  |
true  | false |
true  | true  |

See how we made a row for each possible combination of a and b?  Now
we just need the answers (for the third column)

If a is false and b is false then what is a AND b? Is it true or
false? For example, a could be the statement "grass is purple" (which
is obviously false) and b could be the statement "sky is green" (which
is obviously false)  So when we say "grass is purple AND  sky is
green" would it be false or true?  False, right?

a   |   b   |  a AND b
------+-------+----------
false | false |   false
false | true  |
true  | false |
true  | true  |

If a is false and b is true then what is a AND b? Lets say that a is
the statement "grass is purple" (which is obviously false) and b is
the statement "sky is blue" (which is true)  So when we say "grass is
purple AND sky is blue" would the whole thing be false or true?
False, right?

a   |   b   |  a AND b
------+-------+----------
false | false |   false
false | true  |   false
true  | false |
true  | true  |

We keep doing this until we have all the answers filled in:

a   |   b   |  a AND b
------+-------+----------
false | false |   false
false | true  |   false
true  | false |   false
true  | true  |   true

That's the truth table for "a and b," and whoever looks at it will
instantly know that when we say two things with an AND in between we
mean that the whole sentence is true only when both parts are true
(because every other case is false)

So that's how a truth table works. Let me know if you want to talk

- Doctor Jeremiah, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Logic

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