Math 366 Practice Problems for Final Exam
Autumn 2007
1. Each of the following statements has one of the forms
∼
p
p
∧
q
p
∨
q
p
→
q
p
↔
q
Find the appropriate form and indicate what each statement variable in your choice represents.
(a) If Archibald passes the first exam, then he will not drop the course.
(b) The moon is not made of green cheese.
(c) Harry got out of bed and brushed his teeth.
2. Use truth tables to verify each of the following logical equivalences.
(a)
p
∨
(
∼
p
∧
q
)
≡
p
∨
q
(b)
p
↔
(
p
∧
q
)
≡
p
→
q
(c)
p
→
(
q
∨
r
)
≡
(
p
∧ ∼
q
)
→
r
3. Show that each of the following arguments has a valid argument form by exhibiting such a form.
Explain what each statement variable in your form represents.
(a)
I’ll either get a Christmas bonus or I’ll sell my motorcycle.
If I get a Christmas bonus, then I’ll buy a CD player.
If I sell my motorcycle, then I’ll buy a CD player.
Therefore, I’ll buy a CD player.
(b)
If Christine intends to go to the party, then John will also.
John is not intending to go to the party.
Therefore, Christine is not intending to go to the party.
4.
Determine which of the following argument forms are valid and which are not.
Justify your
answers.
If the form is valid, verify that it is by two methods:
truth tables and step by step
derivations using theorem 1.1.1 and table 1.3.1 from the text.
(a)
p
∨
q
.
.
. p
(b)
p
→
(
q
→
r
)
∼
r
p
.
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 Winter '08
 JOSHUA
 Math, Logic, Prime number, Rational number, pq pq pq

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