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Try It Now

Site: Saylor Academy
Course: CS202: Discrete Structures
Book: Try It Now
Printed by: Guest user
Date: Wednesday, May 14, 2025, 2:25 AM

Description

Work these exercises to see how well you understand this material.

Table of contents

Exercises

  1. Write the following in symbolic notation and determine whether it is a tautology: "If I study then I will learn. I will not learn. Therefore, I do not study".

  2. Describe, in general, how duality can be applied to implications if we introduce the relation ⇐, read "is implied by". We define this relation by (p ⇐ q) ⇔ (q ⇒ p).

 

Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

Solutions

  1. Answer: Let s = I will study, t  = I will learn. The argument is: ((s → t) ∧ (¬t)) → (¬s) , call the argument a.



    Since a is a tautology, the argument is valid.

  2. Answer: In any true statement S, replace; ∧ with ∨, ∨ with ∧, 0 with 1, 1 with 0, ⇐ with ⇒,  and ⇒ with ⇐.  Leave all other connectives unchanged.