9-21
59.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim. Translation into standard
form may be required.
a. Not everybody who was indicted by the grand jury went to trial. (False)
b. Some of the people who did not go to trial are people who were not indicted by the
grand jury.
True.
60.
Using the items in Exercise 9-12 in your text as examples, determine the truth value of the
second claim (below) based on that given for the first claim. Translation into standard
form may be required.
a. Not everybody who was indicted by the grand jury went to trial. (True)
b. Some of the people who did not go to trial are people who were not indicted by the
grand jury.
False.
61.
Reconstruct the following as a standard-form syllogism; then, determine whether it is valid
using either a Venn diagram or the rules of the syllogism.
All legislatures are more influenced by the legal profession than by any other, but it is
legislatures that make the rules by which the legal profession operates. So, the result is
that the bodies that make the rules for the lawyers’ profession are bodies most influenced
by that very profession.
All legislatures are bodies influenced most…
All bodies that make rules… are legislatures.
So, all bodies that make rules… are bodies influenced most…
Valid.
62.
Reconstruct the following as a standard-form syllogism; then, determine whether it is valid
using either a Venn diagram or the rules of the syllogism.
Anyone who wants recordings of music that are faithful to the original will find that CDs
cannot be surpassed; so, you, too, will find that CDs cannot be surpassed.
F = people who want recordings of music that are faithful to the original; C = people who
will find that CDs cannot be surpassed; Y = you.
All F are C.
[All Y are F.]
Therefore, all Y are C.
Valid.
63.
Reconstruct the following as a standard-form syllogism; then, determine whether it is valid
using either a Venn diagram or the rules of the syllogism.
Only those courses that are in the schedule will be offered. Among the courses that will
not be offered is History 105, History of Europe. Therefore, History 105 is not in the
schedule.
S = courses in the schedule; O = courses that will be offered; H = History 105.
All O are S.
No H are O.
Therefore, no H are S.
Invalid.
64.
Reconstruct the following as a standard-form syllogism; then, determine whether it is valid
using either a Venn diagram or the rules of the syllogism.
“No country can vote for a man as President who aims to destroy the system he heads.
That’s why we didn’t support [Stipe] Mesic.” —Borisav Jovic, former president of
Yugoslavia
S = countries that support Mesic; P = countries that can vote for a man as president who
aims to destroy the system he heads; T = this country.
All S are P.
No T are P.
Therefore, no T are S.
Valid.
65.
Reconstruct the following as a standard-form syllogism; then, determine whether it is valid
using either a Venn diagram or the rules of the syllogism.
“Not necessarily, Mr. Dalgliesh. Suppose it’s a double bluff. Suppose he’s saying in effect,
‘Look, I can prove I knew the Whistler was dead. Whoever killed Hilary Robarts didn’t
know. So why aren’t you looking for someone who hadn’t been told that the Whistler’s
body had been found?’” —P. D. James,
Devices and Desires
I = people identical to me; W = people who knew the Whistler was dead; K = people who
killed Hilary Robarts.
No W are K.
All I are W.
Therefore, no I are K.
Valid.
66.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
No Xs are Ys.
Some Ys are not Zs.
So, some Xs are not Zs.
Invalid.
67.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
All Xs are Ys.
No Ys are Zs.
So, no Xs are Zs.
Valid.
68.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
Some Xs are Ys.
No Zs are Ys.
So, some Xs are not Zs.
Valid.
69.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
No coinsurance policies are policies that cover the full value of the property.
Some policies that cover the full value of the property are discounted policies.
So, some discounted policies are not coinsurance policies.
Valid.
70.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
Some early Christians were rationalists.
All early Gnostics were rationalists.
So, some early Gnostics were Christians.
Invalid.
71.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
Everybody who exhibits hubris is an arrogant person.
Some arrogant people are not sympathetic people.
So, some people who exhibit hubris are not sympathetic people.
Invalid.
72.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
All the networks devoted considerable attention to reporting poll results during the last
election, but many of those poll results were not especially newsworthy. So the networks
have to admit that some unnewsworthy items received quite a bit of their attention.
Valid.
73.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
Only people who have lost a job can appreciate the difficulties the loss can cause. Some
of the people in this room have lost jobs in the past, so there are people in this room who
can appreciate the resulting troubles.
Invalid.
74.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
Every vice president has an advantage over his opponent in a presidential election.
Senator Junket is not a vice president, of course, so he cannot have an advantage in the
coming election.
Invalid.
75.
Determine whether the following argument is valid by using either the diagram method or
the rules of the syllogism.
Anything that might indicate an increased risk of heart attack should be taken very
seriously by anyone over forty. So high levels of low-density lipids in the bloodstream
ought to be taken seriously by such people, because they definitely are indicators of
increased risk.
Valid.
76.
Reconstruct the following as a standard-form syllogism, and determine whether it is valid.
Evergreen trees can’t be hardwood, because they aren’t deciduous. Hardwood trees are all
deciduous.
E = evergreen trees; H = hardwood trees; D = deciduous trees.
No E are D.
All H are D.
Therefore, no E are H.
Valid.
77.
Reconstruct the following as a standard-form syllogism, and determine whether it is valid.
In this country, nothing counts except success on the job. And since traditional women’s
work has not counted as a “job,” such work has not been properly appreciated.
X = work that counts (i.e., is appreciated); Y = successful work “on the job”; Z =
traditional women’s work.
All X are Y.
No Z are Y.
Therefore, no Z are X.
Valid.
78.
Reconstruct the following as a standard-form syllogism, and determine whether it is valid.
From a letter to the editor: “Any project that gets taxpayers’ money ought to be one that
the taxpayers get some sort of benefit from, don’t you think? So if the Federal Aviation
Authority is going to pour millions in public funds into automated flight centers at all
privately owned airports, then justice can only be served by forcing those airports to begin
offering services to the public as well as their current wealthy patrons.”
X = automated flight center projects at private airports; Y = projects that get taxpayers’
money;
Z = projects taxpayers should get some benefit from.
All Y are Z.
All X are Y.
Therefore, all X are Z.
Valid.
79.
Reconstruct the following as a standard-form syllogism, and determine whether it is valid.
God, by definition, possesses all perfections. Existence, by definition, is a perfection.
Therefore God, by definition, exists.
P = perfections; A = attributes or characteristics of God; E = the class of things identical
to existence.
All P are A.
All E are P.
Therefore, all E are A.
Valid.
80.
Reconstruct the following as a standard-form syllogism, and determine whether it is valid.
The new dean at Stratford Business School initiated many new policies after taking office.
All of the new policies emphasized employee and customer satisfaction. After a
conversation with the new dean, an associate dean remarked that since none of the
policies of the old curriculum was among those initiated by the dean, the associate dean
had to conclude, to his surprise, that none of the old curriculum policies emphasized
employee and customer satisfaction.
X = new policies initiated by the dean; Z = policies that emphasize employee and
customer satisfaction; Y = policies of the old curriculum.
All X are Z.
No Y are X.
Therefore, all Y are Z.
Invalid.
81.
Reconstruct the following as a standard-form syllogism, and determine whether it is valid.
Slovenia is an independent Balkan country. All of the former parts of Yugoslavia are now
independent Balkan countries, so Slovenia must be a former part of Yugoslavia.
S = countries identical to Slovenia; B = independent Balkan countries; Y = former parts of
Yugoslavia.
All S are B.
All Y are B.
Therefore, all S are Y.
Invalid; breaks rule 2. This item illustrates that an argument’s invalidity is not a reason for
thinking that its conclusion is in fact false.
82.
Reconstruct the following as a standard-form syllogism, and determine whether it is valid.
Being a mathematical prodigy is not enough to guarantee success at solving problems
such as Fermat’s Last Theorem, because several mathematical prodigies tried their hands
at that very problem, and nobody could solve it until just a few years ago.
You have to be careful setting up this one. Here’s how we would do it:
P = mathematical prodigies; S = people who are guaranteed success at solving problems
like Fermat’s Last Theorem; F = people who could not solve Fermat’s Last Theorem.
Some P are F.
No F are S.
Therefore, some P are not S.
Valid.