DEDUCTIVE R= EASONING EXERCISE
Indicate whether the conclusion of each syllogism belo= w is valid or invalid, and whether the syllogism is sound or unsound. If a syllogism is invalid, identif= y the specific rule of deduction that is violated.
Rules for Valid Syllogisms
1)
There must be th=
ree
and only three terms in a syllogism
2)
Definitions of t=
erms
must remain consistent
3)
The middle term =
must
be “distributed” in the major and minor premise (e.g., the subj=
ect
in one, the predicate in the other)
4)
The middle term =
cannot
be included in the conclusion
5)
At least one pre=
mise
must be affirmative
6)
If either premis=
e is
negative, the conclusion must be negative
7)
Both premises ca=
nnot
be negative
8)
If both premises=
are
affirmative, the conclusion must be affirmative
9)
At least one pre=
mise
must be universal
10)
If one premise is
particular, the conclusion must be particular
11)
Each term must a=
ppear
twice
1. If a person has HIV she or he should never have unprotected sex.
Ricky never has unprotected sex
Therefore, Ricky has HIV
2. No dogs are cats
All cats are good at catching mice
Therefore, no dogs are good at catching mice
3. Every short person is left-handed
Eloise is left-handed
Therefore, Eloise is a short person
4. Nadine told me that if she ever got divorced, she w=
ould
move to
Nadine did not move to
Therefore, Nadine did not get divorced.
5. All men are human beings
All women are human beings
Therefore, all men are women
6. 1 is greater than 2
2 is greater than 3
Therefore, 1 is greater than 3
7. Italians are great lovers
Joey is not Italian
Therefore, Joey is not a great lover
8. Some men are triathletes
Some Americans are men
Therefore, some Americans are triathletes
9. What’s mine is mine
What’s yours is mine
Therefore, what’s mine is yours.
10. Some Zimzams are Nimtotes
Some Nimtotes are Hifhafs
Therefore, some Zimzams are Hifhafs
11. All thingamajigs are dealyboppers
No dealyboppers are whatchamucallits
Therefore, no thingamajigs are whatchamucallits
12. No Cathloic favors abortion
Nikki is not a Cathloic
Therefore, Nikki favors abortion
13. All Californians are happy.
Some Californians are Cal State Fullerton students
Therefore some Cal State Fullerton students are happy<= /p>
Other Types o=
f deductive
reasoning (You’ll need to create a grid or “truth table” =
to
solve these)
14. There are three men, each of whom is engaged in a
different occupation. By a strange coincidence their names, Mr. Carpenter, =
Mr.
Mason, and Mr. Painter, are the same as their trades, but not necessarily
respectively.
The following statements were made ab=
out
the three men but it turned out that only one statement was true:
Mr.
Carpenter is not a painter.
Mr. Mason is not a carpenter.
Mr. Carpenter is a carpenter.
Mr. Mason is not a painter.
Who does what?
15. Maleek is considering four different wireless phone
packages. He demands a phone =
that
is small, lightweight, and that has long battery life. He would prefer that there be no c=
ancellation
fee for changing plans, but that isn’t a necessity. He doesn’t care about bonus
frequent flier miles one way or another.&n=
bsp;
He does care about calling costs: If the phone package doesn’t
include a lot of free minutes per month, then it must have a low cost per
minute fee (10 cents per minute or less).&=
nbsp;
He doesn’t care about roaming charges, because he doesn’t
travel much.
The four options he is considering are:
Company A: includes 10,000 =
frequent
flier miles, 500 free minutes per month, a cancellation fee of $100, a smal=
l,
light phone, and long battery life.
Roaming charges apply for out of area calls.
Company B: includes no freq=
uent
flier miles, a 7 cent per minute rate or 300 free minutes per month, no
cancellation fee, a small, light phone, with low battery life. There are no roaming charges for o=
ut of
area calls.
Company C: includes 20,000 =
frequent
flier miles, free unlimited calling, a cancellation fee of $125, a small, b=
ut
heavy phone and very long battery life.&nb=
sp;
There are no roaming charges for out of area calls.
Company D: includes no freq=
uent
flier miles, 20 free minutes per month, a higher 15 cent per minute rate, no
cancellation fee, a medium-sized, 12 ounce phone, with medium battery life.
Roaming charges do not apply for out of area calls.
Given his demands in a phone
provider, which company should Maleek select?
16. Jack has a major crush on Jill. During study hall,=
he
finally gathers all of his courage and writes her a note asking her out on
Saturday night. The note passes to five students (who all read it) before it
gets to Jill. Just as Jill gets the note, Mrs. Wilson the teacher confiscat=
es
it. After reading the note, she wants to know all who were involved in the =
note
passing incident. She questions her students, and receives the following
responses.
The girl studying English passed it to Paul who pass=
ed
it to the girl in green.
Josephine passed it to the boy in blue who gave it to
Alexis who was reading.
The girl in black gave it to Jill.
Jack first gave it to Mary who was studying English.=
The girl in black who was reading got the note from
Derrick.
Mrs. Wilson remembers the following facts fr= om study hall.
Paul was wearing yellow.
Derrick was studying French.
The girl in green was studying science.
From the information given by the students, = can you determine what color each culprit was wearing, the subject they were studying and the order that they received the note? Use the truth table bel= ow to help you.
![3D"http://www.norfacad.pvt.k12.va.us/puzzles/note.gif"](3D"NameThatSyllogism_files/image001.gif")
Answers:
1.invalid: affirming the consequent, and undistributed middle term (having unprotected sex)
2. invalid, because the minor premise doesn’t sa= y only cats are good at catching mice, dogs might be good at it too
3. valid, but unsound because the first premise is fal= se
4. invalid: denying the antecedent and undistributed m= iddle term
5. invalid: undistributed middle term; “human be= ings is the predicate in both premises
6. valid, but unsound because the premises are false
7. invalid: denying the antecedent
8. invalid, no valid conclusion can be drawn from two qualified or particular premises
9. invalid: undistributed middle term
10. invalid: two particular premises
11. valid
12. invalid: two negative premises.
13. valid (conditional or particular premise requires a particular or conditional conclusion)
14.
15.
16.