Thinking Mathematically (6th Edition)

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

Chapter 5 - Number Theory and the Real Number System - 5.5 Real Numbers and Their Properties; Clock Addition - Exercise Set 5.5 - Page 309: 58

Answer

(a) As, \[\left( c\ \square \ d \right)=a\], thus \[\begin{align} & e\ \vartriangle \ \left( c\ \square \ d \right)=e\ \vartriangle \ a \\ & =a \end{align}\] Now, find RHS as, \[\begin{align} & \left( e\ \vartriangle \ c \right)\ \square \ \left( e\ \Delta \ d \right)=d\ \square \ c \\ & =a \end{align}\] Hence, \[e\ \vartriangle \ \left( c\ \square \ d \right)=\left( e\ \vartriangle \ c \right)\ \square \ \left( e\ \Delta \ d \right)\]. (b) As, \[e\ \vartriangle \ \left( c\ \square \ d \right)=\left( e\ \vartriangle \ c \right)\ \square \ \left( e\ \Delta \ d \right)\]and\[e\]is distributed over \[\left( c\ \square \ d \right)\]. Thus, distributive property is used. Hence, distributive property is used in \[e\ \vartriangle \ \left( c\ \square \ d \right)=\left( e\ \vartriangle \ c \right)\ \square \ \left( e\ \Delta \ d \right)\].
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