UMBC CMSC203 Discrete Structures, Section 06, Spring 2016
Homework 4, Due Thursday, 02/25
For this homework assignment, you are asked to provide 3 proofs.
Remember that proofs are written in English. You proof should
not be a sequence of arithmetic equations. There must be a narrative
composed of complete English sentences, correctly punctuated, with
math symbols mixed in as appropriate, which convinces the reader
that the claim is correct.
Give an indirect proof for the following claim:
If m and n are odd integers, then m⋅n
is an odd integer.
Proof by Contradiction.
Prove by contradiction that the following graph is not 3-colorable.
Proof by Cases. [Adapted from Rosen 5/e.]
Let min: R × R → R be the function that
"returns" the minimum of two values.
(Here, R is the set of real numbers.)
min(3.1, 5) = 3.1
min(17.2, 9.4) = 9.4
Prove by cases, that for all real numbers a, b and c,