EECS 310, Fall 2011
Instructor: Nicole Immorlica
Problem Set #1
Due: Sept 27, 2011
1. (15 points) Graph coloring abstraction.
Describe a problem (other than the two mentioned in lecture) that can be solved using
a graph coloring abstraction.
Give a (small) instance of the problem, convert it to a
graph, describe a coloring of your graph, and explain the implied solution.
2. (15 points) Logic.
(a) (5 points) The
exclusive or
operation is defined as:
P
⊕
Q
is true when exactly one
of
P
or
Q
is true. Find an expression equivalent to
P
⊕
Q
using only
not
(
¬
),
and
(
∧
), and
or
(
∨
).
(b) (5 points) The operators
not
(
¬
) and
and
(
∧
) are complete in the sense that any
logical statement can be expressed using only these two operators. Find an expres
sion equivalent to
P
⇐⇒
Q
using only
not
(
¬
) and
and
(
∧
).
(c) (5 points) Rewrite
¬
(
P
→
Q
) using only
not
(
¬
) and
and
(
∧
), distributing the
negation throughout the parathenses (so that the symbol
¬
is followed directly by
P
or
Q
in your final statement).
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 Fall '11
 N/A
 Economics, Alice

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