Chapter 1: Q13SE (page 111)
Suppose that you meet three people Aaron, Bohan, and Crystal. Can you determine what Aaron, Bohan, and Crystal are if Aaron says “All of us are knaves” and Bohan says “Exactly one of us is a knave.”?
The Aaron is a knave and Crystal is a knight, and it cannot be determined what Bohan is.
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Let p, q, and r be the propositions
p : You have the flu.
q: You miss the final examination.
r : You pass the course.
Express each of these propositions as an English sentence.
a)
b)
c)
d)
e)
f )
You are eligible to be President of the U.S.A. only if you are at least 35 years old, were born in the U.S.A, or at the time of your birth both of your parents were citizens, and you have lived at least 14 years in the country. Express your answer in terms of e: “You are eligible to be President of the U.S.A.,” a: “You are at least 35 years old,” b: “You were born in the U.S.A,” p: “At the time of your birth, both of your parents where citizens,” and r: “You have lived at least 14 years in the U.S.A.”
Show that andare not logically equivalent
What Boolean search would you use to look for Web pages about hiking in West Virginia? What if you wanted to find Web pages about hiking in Virginia, but not in West Virginia?
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."
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