Chapter 1: Q17SE (page 111)
Show that the argument with premises “The tooth fairy is a real person” and “The tooth fairy is not a real person” and conclusion “You can find gold at the end of the rainbow” is a valid argument. Does this show that the conclusion is true?
It is a valid argument and the conclusion is not true.
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Explain, without using a truth table, why is true when at least one of p,q, and r is true and at least one is false, but is false when all three variables have the same truth value.
Let be the statement “xhas sent an e-mail message to y,” where the domain for both xand yconsists of all students in your class. Express each of these quantifications in English.
(a) (b)
(c) (d)
(e) (f)
Which of these are propositions? What are the truth values of those that are propositions?
a) Do not pass go.
b) What time is it?
c) There are no black flies in Maine.
d)
e) The moon is made of green cheese.
f)
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.
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
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