Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 3 - Logic - 3.7 Arguments and Truth Tables - Exercise Set 3.7 - Page 194: 76

Answer

The tautology conditional statement has a valid argument and not tautology statement has an invalid argument.

Work Step by Step

The argument that contains two premises and a conclusion is given in a symbolic form is: \[\left[ \left( \text{premise 1} \right)\wedge \left( \text{premises 2} \right) \right]\to \text{conclusion}\] Construct a truth table for the conditional statement for a symbolic statement. If the truth table, the last column has all values true, then the conditional statement is a tautology and the argument is valid, else the conditional statement is not a tautology and the argument is not valid. Hence, the tautology conditional statement has a valid argument and not tautology statement has an invalid argument.
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