Chapter 1: Q56E (page 56)
Given the Prolog facts in Example 28, what would Prolog
return when given these queries?
a) ?enrolled(kevin,ee222)
b) ?enrolled(kiko,math273)
c) ?instructor(grossman,X)
d) ?instructor(X,cs301)
e) ?teaches(X,kevin)
a) No
b) Yes
c) cs301
d) Grossman
e) Chan
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Show that and pare logically equivalent.
A says “The two of us are both knights” and B says A “ is a knave.”
Let p and q be the propositions “The election is decided” and “The votes have been counted,” respectively. Express each of these compound propositions as an English sentence.
a)
b)
c)
d)
e)
f )
g)
h)
Write each of these statements in the form “if p, then q” in English. [Hint: Refer to the list of common ways to express conditional statements provided in this section.]
a) I will remember to send you the address only if you send me an e-mail message.
b) To be a citizen of this country, it is sufficient that you were born in the United States.
c) If you keep your textbook, it will be a useful reference in your future courses.
d) The Red Wings will win the Stanley Cup if their goalie plays well.
e) That you get the job implies that you had the best credentials.
f ) The beach erodes whenever there is a storm.
g) It is necessary to have a valid password to log on to the server.
h) You will reach the summit unless you begin your climb too late.
Let and be the statements “xis a duck,” “xis one of my poultry,” “xis an officer,” and “xis willing to waltz,” respectively. Express each of these statements using quantifiers; logical connectives; andand.
(a) No ducks are willing to waltz.
(b) No officers ever decline to waltz.
(c) All my poultry are ducks.
(d) My poultry are not officers.
(e) Does (d) follow from (a), (b), and (c)? If not, is there a correct conclusion?
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