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: 45

Answer

¬ and ∧ form a functionally complete collection of logical operators.

Work Step by Step

Given a compound proposition p. We can write down a proposition q that is logically equivalent to p and uses only ', /\, and V. Now by De Morgan's law we can get rid of all the /\ 's by replacing each occurrence of P1 /\ P2 /\ · · · /\ Pn with the equivalent proposition -.(-.pi V 'P2 V · · · V 'Pn).
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