Combinations, Permutations and Truth Tables

1. (a) How many license plates can a state produce if the plates can contain 6 characters (from 26 letters and 10 digits) if they can only use one digit? (b) How many ways can Mr. Paul choose 6 students from a class of 15 Boys and 12 Girls, if he must choose at least 5 boys? (c) How many orderings are there of the letter ...continues

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

Please see the attached file for the fully formatted problems. 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 li ...continues

Equivalence Classes

Let P, P' be equivalence relations on a set A. Let n, n' be the number of equivalence classes of p, p', respectively. A) define an equivalence relation p'' as follows: xp''y <=> (xpy) and (xp'y) what is the least number of equivalence classes of p''? What is the greatest number of equivalence classes of p''? B)defin ...continues

Equivalence Relations and Classes

Let L be a subset of {a,b}* Define a relation R (R sub L) on S* as follows: L for All of x, y is a member of S*, (x,y) are members of R if for all of z, xz are members of L iff yz are members of L A) Show that R is an equivalence relation B) Suppose L={a^i b^i where i >= 0} What can you say about the inde ...continues

Set Theory : Proof

(A union B)* = (A*B*)* = (A* union B*)*

Graph Theory.

Show that it is impossible for an odd number of people in a group to each know exactly 2k+1 other people in the group for any integer k.

Let L be a Lattice. Then for every a and b in L (a) a V b = b if and only if a <, or = b (b) a Λ b = a if and only if a <, or = b (c) a Λ b = a if and only if a V b = b

Order Relations and Structures Properties of Lattices Theorem Let L be a Lattice. Then for every a and b in L ...continues

Logical reasoning

Sharky, a leader of the underworld, was killed by one of his own band of four henchmen. Detective Sharp interviewed the men and determined that all were lying except one. He deduced who killed Sharky on the basis of the following statements: a. Socko: Lefty killed Sharky. b. Fats: Muscles didn't kill Sharky c. Lefty: Muscle ...continues

Adjacency Matrix.

Find an adjacency matrix for Kn. (That's K 'sub' n)

Adjacency Matrix.

Find an adjacency matrix for Cn. (That's C 'sub' n)