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    Discrete Math : Probability, Functional Relations, Partitions and Primary Keys

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    Name ________________________________ SSN __________________
    CMSC 203 - Homework Assignment 4 - Due December 9, 2003
    1. (a) Suppose I have a cooler full of cans of Coke, Pepsi, Sprite, Mountain Dew, Dr. Pepper, and
    Slice sodas. How many distinct ways can I line these up on a table if the cooler contains 5 of each
    type of soda?
    (b) Suppose I have a large collection of coins consisting of Pennies, Nickels, Dimes, Quarters,
    Half-Dollars, and Dollars. How many ways can I select distinct combinations of 50 coins if I must
    have 5 of each type in each collection?
    Name ________________________________ SSN __________________
    CMSC 203 - Homework Assignment 4 - Due December 9, 2003
    2. Consider the following sets with corresponding number of elements indicated in each region:
    (a) Find P(A)
    (b) Find P(A | (B Ç C))
    A B
    C
    5 3 8
    7
    2
    6 4
    1 U
    Name ________________________________ SSN __________________
    CMSC 203 - Homework Assignment 4 - Due December 9, 2003
    3. (a) Draw the directed graph of the relation R on A = {1, 2, 3, 4, 5, 6, 7, 8} defined as
    R = {(a,b) | a,b Î A and a º b mod 3}.
    2 3
    · ·
    1· · 4
    8· · 5
    · ·
    7 6
    (b) Find the matrix representing the relation on {1, 2, 3, 4, 5} given by:
    R = {(1,3),(1,5),(2,2),(3,2),(3,4),(4,1),(4,3),(4,5),(5,2),(5,3),(5,4),(5,5)}
    (c) Find MR o MS for the relations on whose matrix
    representations are MR = and MS = .
    1 0 0 0 0 1
    0 0 1 0 1 1
    0 0 1 1 0 0
    0 0 0 1 0 0
    1 1 1 0 0 0
    0 1 0 1 0 1
    0 0 1 0 1 0
    0 1 0 1 1 0
    1 1 0 1 1 0
    1 0 1 1 1 0
    1 0 0 1 0 0
    0 1 0 1 0 0
    Name ________________________________ SSN __________________
    CMSC 203 - Homework Assignment 4 - Due December 9, 2003
    4. Consider the relation, R, on the set A = {a, b, c, d, e, f, g, h} given by the graph:
    (a) Find [d]
    (b) Find the partition of A induced by R
    a
    c e
    g
    h
    f
    d
    b
    Name ________________________________ SSN __________________
    CMSC 203 - Homework Assignment 4 - Due December 9, 2003
    5. Let F be a function on the integers given by F(n) = n2+ 1.
    (a) Show that the relation R = {(x,y) | x,y are integers and F(x) = F(y)}is a Reflexive, Symmetric,
    and Transitive relation.
    (b) Describe the partition of the integers induced by R.
    .
    Name ________________________________ SSN __________________
    CMSC 203 - Homework Assignment 4 - Due December 9, 2003
    6. Consider the database consisting of the following Fields and Records:
    First Name Last Name Age Phone Height (in.) Weight
    Michael Jones 26 555-1234 68 155
    Mary Smith 31 555-4321 65 128
    Ted Green 22 555-6789 74 210
    Susan Green 20 555-6789 69 144
    William Peters 44 555-9876 73 185
    Alan Green 44 555-6789 70 185
    (a) For this database, which Fields would serve as Primary Keys?
    (b) Find P1,4,5
    (c) Find P2,4

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    https://brainmass.com/math/discrete-math/discrete-math-probability-functional-relations-partitions-and-primary-keys-11491

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    Solution Summary

    An assortment of discrete math problems are solved.

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