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 1.4 - Predicates and Quantifiers - Exercises - Page 53: 17

Answer

a) P(0) ∨ P(1) ∨ P(2) ∨ P(3) ∨ P(4) b) P(0)∧P(1)∧P(2)∧P(3)∧P(4) c) ¬P(0)∨¬P(1)∨ ¬P(2) ∨ ¬P(3) ∨ ¬P(4) d) ¬P(0) ∧ ¬P(1) ∧ ¬P(2) ∧¬P(3) ∧ ¬P(4) e) ¬(P (0) ∨ P(1) ∨ P(2) ∨ P(3) ∨ P(4)) f) ¬(P (0) ∧ P(1) ∧ P(2) ∧ P(3) ∧ P(4))

Work Step by Step

Writing each of the given propositions using disjunctions, conjunctions,and negations. a) P(0) ∨ P(1) ∨ P(2) ∨ P(3) ∨ P(4) b) P(0)∧P(1)∧P(2)∧P(3)∧P(4) c) ¬P(0)∨¬P(1)∨ ¬P(2) ∨ ¬P(3) ∨ ¬P(4) d) ¬P(0) ∧ ¬P(1) ∧ ¬P(2) ∧¬P(3) ∧ ¬P(4) e) ¬(P (0) ∨ P(1) ∨ P(2) ∨ P(3) ∨ P(4)) f) ¬(P (0) ∧ P(1) ∧ P(2) ∧ P(3) ∧ P(4))
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