11) Use generating functions to determine the number of different ways
12 identical action figures can be given to five children so that each
child receives at most three action figures.
12) Use generating functions to find the number of ways to select 10
balls from an urn containing red, white and blue balls if:
a. The selection has at least two balls of each color.
b. The selection has at most two balls of each color.
c. The selection has an even number of red balls.
13) Determine whether the relation R on the set of all real numbers is
reflexive, symmetric, antisymmetric, and/or transitive, where (x,y) E R,
if and only if:
a) x + y = 0
b) xy = 0
14) Find:
a) R1 U R3
b) R1 - R2
c) R2 (symmetric difference) R4
15) Show that the sum, over the set of people at a party, of the number
of people a person has shaken hands with, is even.? ASsume that no one
shakes his or her own hand.
16) What is the sum of the entries in a column of the adjacency matrix
for an undirected graph?? For a directed graph?
17) Show that the PETERSON GRAPH, does not have a Hamilton circuit, but
that the subgraph obtained by deleting a vertex v, and all edges
incident with v, does have a Hamilton circuit.
Mathematics Homework Solutions
#5612
Discrete Structures
11) Use generating functions to determine the number of different ways 12 identical action figures can be given to five children so that each child receives at most three action figures.
12) Use generating functions to find the number of ways to select 10 balls from an urn containing red, white and blue balls if:
a. The selection has at least two balls of each color.
b. The selection has at most two balls of each color.
c. The selection has an even number of red balls.
13) Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x,y) E R, if and only if:
a) x + y = 0
b) xy = 0
14) Find:
a) R1 U R3
b) R1 - R2
c) R2 (symmetric difference) R4
15) Show that the sum, over the set of people at a party, of the number of people a person has shaken hands with, is even.? Assume that no one shakes his or her own hand.
16) What is the sum of the entries in a column of the adjacency matrix for an undirected graph?? For a directed graph?
17) Show that the PETERSON GRAPH, does not have a Hamilton circuit, but that the subgraph obtained by deleting a vertex v, and all edges incident with v, does have a Hamilton circuit.
The solution contains detailed explanations of whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive. Some problems in graph theory are discussed as well.
What is this?
By OTA - Overall OTA Rating
Changping Wang, MA - 4.9/5
Purchase Cost Now
$2.19 CAD (was ~$15.96)
Included in Download
- Plain text response
Why you can trust BrainMass.com
- Your Information is Secure
- Best Online Academic Help Service
- Students find real academic Success
- Discrete mathematics - List 16 different relations on the set {0,1} as sets of pairs. State if they are reflexive, transitive, symmetric, antisymmetric
- Binary Relations. - Determine whether the binary relation R on Z, where aRb means |a-b| <= 1, is reflexive, symmetric, antisymmetric, and/or transitive.
- Determine reflexive, symmetric, antisymmetric, transitive, partial order and equivalence. - Let R = {(1,1)(3,1)(2,2)(1,2)(3,3)(3,2)} on Z = {1,2,3} Is R reflexive? Why? Is R Symmetric? Why? Is R antisymmetric? Why? Is R transitive? Why? Is R a partial order? Why? Is R an equivalence ...
- Discrete Mathematics and Its Applications - On the following terms could you please give my an English text description - in your own words. Thanks. 1. Combinatorics: 2. Enumeration: 3. Permutation: 4. Relation on A: 5. Rn: 6. Reflexive ...
- A binary relation R is defined in terms of a given matrix. Define what it means for a relation to be (a) reflexive, (b), antisymmetric, and (c) transitive. Also, determine which of these are properties of R. - For the set A = {a, b, c}, let R be the relation on A which is defined by the following 3 by 3 matrix M_R: ---------------------------------------- Row 1: 1 0 1 Row 2: 1 1 0 Row 3: 0 1 1 ...
