MAD 2104
March 30, 2000
Exam 3
Prof. S. Hudson
Name
Try to answer the questions in the space provided.
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Do not use a calculator, book, or any personal
paper. You may ask about any ambiguous questions or for extra paper. If you use extra
paper, be sure to hand it in with your exam.
1) (15pts) a) How many functions are there from a set of 3 elements to a set of 8 elements?
b) How many onetoone functions are there from a set of 3 elements to a set of 8 elements?
c) How many onto functions are there from a set of 3 elements to a set of 8 elements?
2) (15pts) The inclusion relation,
R
=
{
(
A, B
)

A
⊆
B
}
is a relation on the set of subsets
of
Z
.
a) Is
R
reflexive? Briefly justify your answer.
b) Is
R
antisymmetric? Briefly justify your answer.
c) Is
R
a partial order? Briefly justify your answer.
1
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3) (10pt) Determine whether the two graphs below are isomorphic (either give an isomor
phism
f
, or find an invariant they don’t share).
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 Fall '08
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 Equivalence relation, Binary relation, Transitive relation, Prof. S. Hudson

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