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 3.4 - Page 142: 3

Answer

The conclusion: $\therefore \frac{2}{3} + \frac{4}{5} = \frac{(2\cdot 5 +3 \cdot 4)}{3 \cdot 5}$

Work Step by Step

Universal modus ponens: $\forall x,$ if $P(x)$ then $Q(x)$. $P(a)$ for a particular $a$. $\therefore Q(a).$ In this case, P(x) is: for all real numbers a, b, c, and d, if $b \neq 0$ and $d \neq 0$. Q(x) is: a/b + c/d = (ad + bc)/bd. Plug in the particular values for a, b, c, and d (2, 3, 4, 5 respectively) into Q to obtain the conclusion: $\therefore \frac{2}{3} + \frac{4}{5} = \frac{(2\cdot 5 +3 \cdot 4)}{3 \cdot 5}$.
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