Massachusetts Institute of Technology
6.042J/18.062J, Spring ’11
: Mathematics for Computer Science
March 14
Prof. Albert R Meyer
revised Monday 14
th
March, 2011, 23:00
Problem Set 6
Due
: March 30
Reading:
Chapter
9.5
–
9.9
, Partial Orders; Chapter
11
–
11.6
, Simple Graphs.
Skip
Chapter
10
, Communication Nets, which will not be covered this term.
Problem 1.
Let
R
1
,
R
2
be binary relations on the same set,
A
. A relational property is preserved under product, if
R
1
R
2
has the property whenever both
R
1
and
R
2
have the property.
(a)
Verify that each of the following properties are preserved under product.
1. reflexivity,
2. antisymmetry,
3. transitivity.
(b)
Verify that if
either
of
R
1
or
R
2
is irreflexive, then so is
R
1
R
2
.
Note that it now follows immediately that if if
R
1
and
R
2
are partial orders and at least one of them is
strict, then
R
1
R
2
is a strict partial order.
Problem 2.
The most famous application of stable matching was in assigning graduating medical students to hospital
residencies. Each hospital has a preference ranking of students and each student has a preference order of
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 Spring '11
 Leighton
 Computer Science, Equivalence relation, Binary relation, Total order, Albert R Meyer

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