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 1.5 - Nested Quantifiers - Exercises - Page 65: 11

Answer

a) A(Louis, Professor Michaels) b) ∀x(S(x)->A(x, Professor Gross) c) ∀x(F(x)->(A(x, Professor Miller) V A(Professor Miller, x))) d) ∃x∀y(S(x)^F(y)->¬A(x,y)) e) ∃x∃y(S(x)^F(y)->¬A(x,y)) f) ∃x∀y(S(x)^F(y)->A(x,y)) g) ∃x∀y((F(x)^F(y)->A(x,y)) h) ∃x∃y(F(x)^S(y)->¬A(x,y))

Work Step by Step

a) A(Louis, Professor Michaels) b) ∀x(S(x)->A(x, Professor Gross) c) ∀x(F(x)->(A(x, Professor Miller) V A(Professor Miller, x))) d) ∃x∀y(S(x)^F(y)->¬A(x,y)) e) ∃x∃y(S(x)^F(y)->¬A(x,y)) f) ∃x∀y(S(x)^F(y)->A(x,y)) g) ∃x∀y((F(x)^F(y)->A(x,y)) h) ∃x∃y(F(x)^S(y)->¬A(x,y))
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