Thinking Mathematically (6th Edition)

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

Chapter 3 - Logic - Chapter 3 Test - Page 209: 25


Argument is Valid.

Work Step by Step

An argument consists of two parts which are called the premises and a conclusion. An argument is called valid argument if conclusion is true whenever the premises are assumed to be true. Consider the simple statements in the argument with a letter: \[p\]: I am sick. \[q\]: I am tired. Express the premises and the conclusion symbolically as I am sick or I am tired: \[p\vee q\] \[\frac{\text{ I am not tired}}{\therefore \text{I am sick}\text{.}}\]: \[\frac{\tilde{\ }q}{\therefore p}\] Write a symbolic statement of the following form: \[\left[ \left( \text{premise}\ \text{1} \right)\wedge \left( \text{premise}\ \text{2} \right) \right]\to \text{conclusion}\] The symbolic statement is \[\left( p\vee q \right)\wedge \left( \tilde{\ }q \right)\to p\]
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