Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.3 - Propositional Equivalences - Exercises - Page 36: 65

Answer

CHECK STEP BY STEP WORK

Work Step by Step

We just repeat the discussion in the text, with the roles of the rows and columns interchanged: To assert that column j contains the number n. We form v;=1 p(i,j,n). To assert that column j contains all 9 numbers. We form the conjunction of these disjunctions over all nine possible values of n, giving us /\~=l Vi=l p( i, j, n). To assert that every column contains every number, we take the conjunction of /\~=l Vi=1 p(i,j,n) over all nine columns. This gives us /\~= 1 /\~= 1 v;=1 p( i, j, n).
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