Discrete Mathematics Answers

1. Proof that an undirected graph has an even number of vertices of odd degree.

Describe at least one way to generate all the partitions of a positive integer n.

1. Discuss ways in which the current telephone numbering plan can be extended to accommodate the rapid demand for more telephone numbers. (See if you can find some of the proposals coming from the telecommunications industry.) For each new numbering plan you discuss, show how to find the number of different telephone numbers it supports.

Prove the statement by contraposition, if a product of two positive real numbers is greater

than 100, then at least one of the numbers is greater than 10.

For all integers n and m, if n − m is even then n^3 − m^3

is even.

An investor is considering a $25,000 investment in a start-up company. She estimates that she has

probability 0.05 of a $15,000 loss, probability 0.15 of a $20,000 loss, probability 0.35 of a $35,000 profit,

and probability 0.45 of breaking even (a profit of $0). What is the expected value of the profit?

Counting subsets of Finite sets: A student can choose a computer project from one of

three lists. The three lists contain 23, 15 and 19 possible projects, respectfully. No project is

on more than one list. How many possible projects are there to choose from?

Suppose that the universal set is U = {1, 2, 3, 4,5, 6, 7, 8, 9, 10}. Express each of these sets with bit

strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.

how to solve power set? {12,34,{45}, 56}