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Deliverable Length: 4 Parts: See Assignment Details

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Weekly tasks or assignments (Individual or Group Projects) will be due by Monday and late submissions will be assigned a late penalty in accordance with the late penalty policy found in the syllabus. NOTE: All submission posting times are based on midnight Central Time.

Task Background: This assignment involves solving problems by using various discrete techniques to model the problems at hand. Quite often, these models form the foundations for writing computer programming code that automate the tasks. To carry out these tasks effectively, a working knowledge of sets, relations, graphs, finite automata structures and Grammars is necessary.

Part I: Set Theory

Look up a roulette wheel diagram. The following sets are defined:

A = the set of red numbers

B = the set of black numbers

C = the set of green numbers

D = the set of even numbers

E = the set of odd numbers

F = {1,2,3,4,5,6,7,8,9,10,11,12}

From these, determine each of the following:

A∪B

A∩D

B∩C

C∪E

B∩F

E∩F

Part II: Relations, Functions, and Sequences

The implementation of the program that runs the game involves testing. One of the necessary tests is to see if the simulated spins are random. Create an n-ary relation, in table form, that depicts possible results of 10 trials of the game. Include the following results of the game:

Number

Color

Odd or even (note: 0 and 00 are considered neither even nor odd.)

Also include a primary key. What is the value of n in this n-ary relation?

Part III: Graphs and Trees

Create a tree that models the following scenario. A player decides to play a maximum of 4 times, betting on red each time. The player will quit after losing twice. In the tree, any possible last plays will be an ending point of the tree. Branches of the tree should…...

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