Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 3 - The Logic of Quantified Statements - Exercise Set 3.1 - Page 106: 11

Answer

The statement is false when $m=1$ and $n=2$.

Work Step by Step

Written in standard english, the logical statement $\forall$ means "for all". Therefore, the statement we are trying to disprove is "For all positive integers $m$ and $n$, $m\cdot n≥m+n$" When we plug $1$ in for $m$ and $2$ in for $n$, we get $1\cdot2≥1+2\Rightarrow2≥3$, which is false. Therefore, the statement is false when $m=1$ and $n=2$.
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