Chapter 1: Q20E (page 35)
Show that and are logically equivalent.
Use truth tables to show that the two expressions have the same truth values for all possible truth values p of and q
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When does , where s is a compound proposition
Write each of these propositions in the form “p if and only if q” in English.
a) If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside.
b) For you to win the contest it is necessary and sufficient that you have the only winning ticket.
c) You get promoted only if you have connections, and you have connections only if you get promoted.
d) If you watch television your mind will decay, and conversely.
e) The trains run late on exactly those days when I take it.
Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the outputfrom input bitsand p,q,r
You can graduate only if you have completed the requirements of your major and you do not owe money to the university and you do not have an overdue library book. Express your answer in terms of g: “You can graduate,” m: “You owe money to the university,” r: “You have completed the requirements of your major,” and b: “You have an overdue library book.”
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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