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 68: 43

Answer

∀m∀b(m = 0 → ∃x(mx + b = 0 ∧ ∀w(mw + b = 0 → w = x)))

Work Step by Step

we have to use quantifiers and logical connectives to express the fact that every linear polynomial (that is, polynomial of degree 1) with real coefficients and where the coefficient of x is nonzero, has exactly one real root. as ∀m∀b(m = 0 → ∃x(mx + b = 0 ∧ ∀w(mw + b = 0 → w = x)))
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