- Propositional Logic (Review)
CS160: Foundations in Programming
The purpose of this lab is to:
- Review propositional logic and truth tables.
- Review logical equivalences and some definitions.
- Do an equivalence proof two different ways.
Create a file called R12.txt and write your solution in it to 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 problem correctly.
- Translate the given statement into propositional logic using the propositions provided:
You can use the wireless network in the airport if you pay the daily fee
or 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."
- Use truth tables to prove these equivalences, and state the name:
- p ∧ T is equivalent to p
- p ∧ F is equivalent to F
- p ∧ p is equivalent to p
- p ∨ (p ∧ q) is equivalent to p
- Use De Morgan's law to find the negation of each of the following
conditions in Java, and shown the resulting condition in Java:
- (i < 1 || i > 9)
- (p != false && q == false)
- Show that the following conditional statement is a tautology by
using truth tables.
- ¬p → (p → q)
- Define tautology, contradiction, and contingency.
- Show the converse, contrapositive, and inverse of p → q.
- Prove the following logical equivalence using only the logical equivalences
and laws on the Logic Sheet.
p ∨ (¬p ∧ q) ≡ (p ∨ q)
- Prove the logical equivalence above using a truth table.
The TA will check off your answers, also please submit your R12.txt to RamCT to verify your attendance.
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