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