Truth Tables: a AND bDate: 09/10/2001 at 22:43:08 From: Emilee Longfellow Subject: Truth Tables I am having trouble finding out what truth tables are. Thank you for your help, Emilee 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 answer. 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 about this some more. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/ |
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