Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 3 - Logic - 3.6 Negations of Conditional Statements and De Morgan's Law - Exercise Set 3.6: 22

Answer

If you cannot literally taste music or cannot smell colors, then you do not suffer from synesthesia.

Work Step by Step

If you suffer from synesthesia, you can literally taste music and smell colors. Let p, q, and r represent the following simple statements: p: You suffer from synesthesia. q: You can literally taste music. r: You can smell colors. The given conditional statement can be represented in symbolic form as: p → (q ᴧ r) An equivalent statement is the contrapositive: ~(q ᴧ r) → ~p Using De-morgan's law, we find: (~q v ~r) → ~p If you cannot literally taste music or cannot smell colors, then you do not suffer from synesthesia.
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