Name:
CSUSM Math 370
Instr: Dr. Andr´
e K¨undgen
SAMPLE ONLY
Final Exam
Show work,
explain your reasoning
and clearly mark your answers.
Please ask
about anything that is unclear. Use back sides of pages for scratch and overflow work, but
clearly indicate which is which!
1.
Short answers questions.
(24 pts)
a) Prove that the product of two odd numbers is odd.
b) Give the proper definition of the symmetric difference of two sets
A, B
.
c) State the Binomial Theorem. (Don’t forget the hypothesis!)
d) What does it mean for a function
f
:
A
→
B
to be onto? (Your answer should
use only symbols and no words.)
e) Give a set
A
such that
{
4
} ∈
A
and
{
4
} ⊆
A
, or explain why such a set can’t
exist.
f) Determine the number of partitions of the set
{
1
,
2
,
3
}
.
2.
Prove that 5
n

1 is divisible by 4, for every natural number
n
.
(10 pts)
3.
Circle all the properties which
R
=
{
(1
,
2)
,
(2
,
4)
,
(3
,
4)
,
(1
,
4)
,
(5
,
7)
,
(6
,
7)
}
satisfies.
(No proof needed)
(10 pts)
R
is reflexive.
R
is irreflexive.
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 Spring '08
 RAMASWAMY
 Math, Vertex, Equivalence relation, Binary relation, Transitive relation

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