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Truth Table Examples

    In this topic we illustrate the process of building truth tables. In terms of a truth table, statements p and q are called variables truth table examples _gr_1.gif]By definition, a proposition whose value is true for all cases of all variables is called a tautology; a proposition whose value is false for all cases of all variables is called a contradiction; and a proposition whose value depends on a value of a variable is called a contingency. Note that all four operations, And, Or, Not, and Implication are all contingencies. It is interesting to also note that we can take a combination of contingency statements and build a contradiction or a tautology. Recall that the contrapositive of truth table examples _gr_2.gif] is the statement truth table examples _gr_3.gif] and the converse of truth table examples _gr_4.gif] is the statement truth table examples _gr_5.gif]
    In this topic we will construct the truth tables for three tautologies, three contradictions, and three contingencies.

Example (Truth Table for a Tautology) Construct a truth table for the following statements.

(a) Tautology:  
    
truth table examples _gr_6.gif]

(b) Tautology:  
    
truth table examples _gr_7.gif]

(c) Tautology:  
    
truth table examples _gr_8.gif]
truth table examples _gr_9.gif]

Example (Truth Table for a Contradiction) Construct a truth table for the following statements.

(a) Contradiction:  
    
truth table examples _gr_10.gif]

(b) Contradiction:  
    
truth table examples _gr_11.gif]

(c) Contradiction:  
    
truth table examples _gr_12.gif]
truth table examples _gr_13.gif]

Example (Truth Table for a Contingency) Construct a truth table for the following statements.

(a) Contingency:  
    
truth table examples _gr_14.gif]

(b) Contingency:  
    
truth table examples _gr_15.gif]

(c) Contingency:  
    
truth table examples _gr_16.gif]
truth table examples _gr_17.gif]

Cite this as:
Truth Table Examples
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/truth-table-examples.html
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