Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 2 - The Logic of Compound Statements - Exercise Set 2.2: 23

Answer

Converses: a. If P is a rectangle then P is a square b. If tomorrow is January, then today is New Year's eve. c. If r is rational, then the decimal expansion of r is terminating. d. If n is odd or if n is 2, then n is prime e. If x is positive or if x is 0, then x is non-negative f. If Jim is Ann;s uncle and Sue is her aunt, then Tom is her father g. If n is divisible by 2 and n is divisible by 3, then n is divisible by 6 Inverses: a. If P is not a square then P is not a rectangle b. If today is not New Year's eve, then tomorrow is not January. c. If the decimal expansion of r is not terminating, then r is not rational. d. If n is not prime, then n is not odd and is not equal to 2 e. If x is not non-negative, then x is not positive and if x is not 0 f. If Tom is not Ann's father, then Jim is nother uncle or Sue is not her aunt g. If n is not divisible by 6, then n is not divisible by 2 or n is divisible by 3

Work Step by Step

Converse of the statement p → q is q → p Inverse of the statement p → q is ~p → ~q Note that even if the statement is true, the inverse and the converse may not be true. Also not that ~(q and r) ≡ ~q or ~r And that, ~(q or r) ≡ ~q and ~r
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