Chapter 1: Q36E (page 91)
Show that the propositions \(p1, p2, p3\), and \(p4\) can be shown to be equivalent by showing that \(p1 \leftrightarrow p4, p2 \leftrightarrow p3, and p1 \leftrightarrow p3\).
The propositions\(p1, p2, p3\), and \(p4\)are equivalent.
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Express these system specifications using the propositions p "The user enters a valid password," q "Access is granted," and r "The user has paid the subscription fee" and logical connectives (including negations).
a) "The user has paid the subscription fee, but does not enter a valid password."
b) "Access is granted whenever the user has paid the subscription fee and enters a valid password."
c) "Access is denied if the user has not paid the subscription fee."
d) "If the user has not entered a valid password but has paid the subscription fee, then access is granted."
Let be the statement “Student xhas taken class y,” where the domain for both xconsists of all students in your class and for yconsists of all computer science courses at your school. Express each of these quantifications in English.
(a) (b)
(c) (d)
(e) (f)
Let p and q be the propositions
p: You drive over 65 miles per hour.
q: You get a speeding ticket. Write these propositions using p and q and logical connectives (including negations).
a) You do not drive over 65 miles per hour.
b) You drive over 65 miles per hour, but you do not get a speeding ticket.
c) You will get a speeding ticket if you drive over 65 miles per hour.
d) If you do not drive over 65 miles per hour, then you will not get a speeding ticket.
e) Driving over 65 miles per hour is sufficient for getting a speeding ticket.
f) You get a speeding ticket, but you do not drive over 65 miles per hour.
g) Whenever you get a speeding ticket, you are driving over 65 miles per hour.
Determine whether these biconditionals are true or false.
a)if and only if
b)if and only if
c)if and only if monkeys can fly.
d) if and only if
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.”
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