Discrete Mathematics
Phase 5 Individual Project
03/23/2014
Math 203
PPCC
Part I: 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}
Answers:
AUB- {All BLACK and RED numbers}
A∩D- {All numbers that are both RED and EVEN}
B∩C- {NO numbers intersect between these two sets}
CUE- {All ODD numbers and 00, 0}
B∩F- {2,4,6,10,11}
E∩F- {1,3,5,7,9,11}
Part II: 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?
The primary key is the trial attempts, the reason for this is because only one attempt can be linked to that trial attempt, therefore making it unique. The value of n is four.
Part III: 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 indicate the winning or losing, and how that affects whether a new play is made.
Part IV: (1) A gate with three rotating arms at waist height is used to control access to a subway in New York city. Initially, the arms of the gate are locked preventing customers from passing through. Unlocking the arms requires depositing a token in a slot, which allows the arms to rotate to a complete turn which allows one customer to push through and enter. Once
03/23/2014
Math 203
PPCC
Part I: 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}
Answers:
AUB- {All BLACK and RED numbers}
A∩D- {All numbers that are both RED and EVEN}
B∩C- {NO numbers intersect between these two sets}
CUE- {All ODD numbers and 00, 0}
B∩F- {2,4,6,10,11}
E∩F- {1,3,5,7,9,11}
Part II: 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?
The primary key is the trial attempts, the reason for this is because only one attempt can be linked to that trial attempt, therefore making it unique. The value of n is four.
Part III: 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 indicate the winning or losing, and how that affects whether a new play is made.
Part IV: (1) A gate with three rotating arms at waist height is used to control access to a subway in New York city. Initially, the arms of the gate are locked preventing customers from passing through. Unlocking the arms requires depositing a token in a slot, which allows the arms to rotate to a complete turn which allows one customer to push through and enter. Once
References: Johnsborough, R. (2009) Discrete Mathematics 7th Edition. (N.D.) Binary search algorithm. Retrieved on March 24, 2014 from https://www.princeton.edu/~achaney/tmve/wiki100k/docs/Binary_search_algorithm.html (November 24, 2011). Computer Algorithms: Sequential Search. Retrieved on March 24, 2014 from http://www.stoimen.com/blog/2011/11/24/computer-algorithms-sequential-search/