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.

  1. Indirect Proof. Give an indirect proof for the following claim:
    If m and n are odd integers, then mn is an odd integer.

  2. Proof by Contradiction. Prove by contradiction that the following graph is not 3-colorable.

  3. Proof by Cases. [Adapted from Rosen 5/e.]
    Let min: R × RR be the function that "returns" the minimum of two values. (Here, R is the set of real numbers.)

    For example,

    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, that

    min(min(a, b), c) = min(a, min(b, c))

Last Modified: 25 Feb 2016 21:44:48 EST by Richard Chang
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