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: 4


The conclusion: $\therefore$ $(3^{1/2})^6 = 3^{(1/2)\cdot 6} = 3^3$.

Work Step by Step

Universal modus ponens: ∀x, if P(x) then Q(x). P(k) for a particular k. ∴Q(k). In this case P(x) is: $\forall$ real numbers r, a, and b, if r is positive. Q(x) is: $(r^a)^b = r^{ab}.$ k are the particular values for r, a, and b (3, 1/2, 6 respectively). Therefore Q(k) is: $(3^{1/2})^6 = 3^{(1/2)\cdot 6} = 3^3$.
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