Thinking Mathematically (6th Edition)

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

Chapter 3 - Logic - 3.2 Compound Statements and Connectives - Exercise Set 3.2 - Page 134: 99

Answer

The dominance of connectives is used to clarify the means of the statement. The ascending order in which dominance of connectives is used is: (1) Negation,\[\sim \] (2) Disjunction, \[\vee \] Conjunction,\[\wedge \] (3) Conditional,\[\to \] (4) Biconditional, \[\leftrightarrow \] Biconditional statement is the most dominant and Negation statement is least dominant and conjunction, disjunction has the same level of dominance. Use this order of dominance of connectives then the statement in the clarify form is: \[\left( p\to p \right)\leftrightarrow \left[ \left( p\wedge p \right)\to \sim p \right]\]. The statement is biconditional because biconditional is most dominant. Hence, the statement in the clarify form is\[\left( p\to p \right)\leftrightarrow \left[ \left( p\wedge p \right)\to \sim p \right]\].

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