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Symbolic Statement - Abstract Mathematics

by Margaret Kiss
(Milford, NY)











































Abstract Mathematics - Symbolic Logic

A symbolic statement represents a symbolic assertion. That assertion is a complete statement which will stand alone. It is either true or false.

Write a symbolic statement for "it is false that if the apartment is hot the air conditioner is not working".

Comments for Symbolic Statement - Abstract Mathematics

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Mar 19, 2013
Symbolic Logic
by: Staff


Answer



c = air conditioner NOT working

h = apartment hot

"it is false that if the apartment is hot the air conditioner is not working"

The Boolean expression for this statement can be written:

“NOT” = (written as ~) a negation

“Conditional If-Then” = (written as ) If the statement preceding this symbol is true, then the statement following this statement is also true.

"T" = True

"F" = False

Boolean Expression:   it is false that if the apartment is hot the air conditioner is not working




The purpose of logic is to enable you to construct valid arguments which satisfy your basic premise: "If all of your premises are true, then the your conclusion must also be true."


This relationship can be also expressed in a “Truth Table”.

A truth table is a list of every possible combination of input values and the output value for each combination. It is a picture of every possibility.

A “Truth Table” for your problem statement looks like this:

Truth Table


Truth Table:   it is false that if the apartment is hot the air conditioner is not working









Thanks for writing.

Staff
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