Colorado State University

Recitation R12 - Inference Rules
Fall 2013

CS160: Foundations in Programming

The purpose of this lab is to:
Solve each of the following problems, one at a time. When everyone has had a chance to go through the problems, your TA will show you how to work each correctly.
  1. Translate the given statement into propositional logic using the propositions provided:

    To use the wireless network in the airport you must pay the daily fee unless you are a subscriber to the service. Express your answer in terms of w: "You can use the wireless network in the airport," d: "You pay the daily fee," and s: "You are a subscriber to the service."

  2. Use truth tables to verify these equivalences.
    1. p ∧ T is equivalent to p
    2. p ∨ T is equivalent to T
    3. p ∧ F is equivalent to F
    4. p ∨ F is equivalent to p
    5. p ∧ p is equivalent to p
    6. p ∨ p is equivalent to p

  3. Use De Morgan's law to find the negation of each of the following statements.
    1. James is young and strong.
    2. Rita will move to Oregon or Washington.

  4. Show that each of these conditional statements is a tautology by using truth tables.
    1. ¬p → (p → q)
    2. (p ∧ q) → (p → q)

  5. Define tautology, contradiction, and contingency.

  6. Show the converse, contrapositive, and inverse of p → q.

  7. Prove the following Rules of Inference. Use a truth table for each and show the equivalence.
  8. Prove the following using the Rules of Inference. State the specific rule for each step.
  9. Prove the previous problem using a truth table.
Show your work to the TA for grading and to get credit for this lab.
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