CS123
March 4, 2010
Youssef
Homework 3
Due Date: March 30, 2010
Problem 1: (20 points)
For each of the following 4 relations on the set L of all living people on Januray 1, 2010,
state (no proof necessary) if the relation is reﬂexive, symmetric, antisymmetric, transitive,
equivalence relation, and/or partial order. In the case of equivalence relations, explain what
every equivalence class signiﬁes. In the case of partial orders, indicate if the set L has a
minimum, a maximum, minimals, and/or maximals, and explain what minimum, maximum,
minimal and maximal mean in that context.
a)
x R y if x is taller than y or x is the same person as y.
b)
x R y if x and y have the same ﬁrst name.
c)
x R y if x graduated from the same university as y.
d)
x R y if the annual income of x is less than that of y or x is the same person as y.
Problem 2: (20 points)
Let
f
be a realvariable function where
f
(
x
) =
x
2
+ 2
x
+ 5, and let
E
=
{
5
,

4
,

3
,

2
,

1
,
0
,
1
,
2
,
3
,
4
,
5
}
. Deﬁne the relation
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Graph Theory, Equivalence relation, Binary relation, Transitive relation, Partition of a set, Eulerian Cycle

Click to edit the document details