Chapter 1: Q48E (page 16)
Is the assertion “This statement is false” a proposition?
This statement is false is not a proposition.
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Suppose that Prolog facts are used to define the predicates mother and father ,which represent that Mis the mother of Yand Fis the father of X, respectively. Give a Prolog rule to define the predicate sibling , which represents that Xand Yare siblings (that is, have the same mother and the same father).
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."
Use a truth table to verify the first De Morgan law.
An explorer is captured by a group of cannibals. There aretwo types of cannibals-those who always tell the truthand those who always lie. The cannibals will barbecuethe explorer unless he can determine whether a particular cannibal always lies or always tells the truth. He isallowed to ask the cannibal exactly one question.
a) Explain why the question "Are you a liar?" does notwork.
b) Find a question that the explorer can use to determinewhether the cannibal always lies or always tells thetruth.
What is the value of x after each of these statements is encountered in a computer program, if x = 1 before the statement is reached?
a) if then
b) if OR then
c) if AND then
d) if XOR then
e) if x < 2 then
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