Proving a partial order and total order.

In each of the following say whether or not R is a partial order on A. If so, is it a total order? a) A= {a,b,c,d}, R= {(a,a),(b,a),(b,b),(b,c),(c,c)} b) A is the set of positive divisors of 24, that is A= {1,2,3,4,6,8,12,24}, and the relation R is dividing. If B is the set of positive divisors of 24 except 1, what is the ...continues

Proving a partial order and total order.

Say whether or not R is a partial order and a total order on A. Show proof. A= {a,b,c}, R= {(a,a),(b,a),(b,b),(b,c),(c,c)

Discrete Math

Discrete math questions. Please provide formulas and all calculations for all 22. They are very short answer type questions.

Equivalence Relation, equivalence classes and the partition defined by the relation.

Verify the relation R on Z defined by xRy iff 5(x-y), i.e., 5 divides x-y, is an equivalence relation. Describe the equivalence classes, and the partition defined by this equivalence relation.

Discrete Math: Mathematical Induction

Please see the attached file for the fully formatted problem. Without using Theorem 4.2.2, use mathematical induction to prove that P(n): 1 + 5 + 9 + ... + (4n - 3) = n(2n - 1) for all integers n >= 1

Discrete Math: Binary Relations

Please see the attached file for the fully formatted problems. 2. Let C = {2, 3, 4, 5} and D = {3, 4} and define a binary relation S from C to D as follows: for all (x, y) for all (x, y)  C  D, (x, y)  S  x  y (Yes/No answers sufficient; explanation optional) a. Is 2 S ...continues

Discrete Math: Binary Relations

Please see the attached file for the fully formatted problems. SECTION 10.2 For #2: A binary relation is defined on the set A = {0, 1, 2, 3}. For the relation given, a. draw the directed graph (See drawing tips in the Overview) b. determine whether the relation is reflexive c. determine whether the relation is symmetr ...continues

discrete math

Discrete math, see attachment

Trees and Graphs: Does the Graph Exist?

Graphs and trees Section 11.5, #16 Either draw a graph with the given specifications or explain why no such graph exists. #16: tree, twelve vertices, fifteen edges Section 11.5, #18 Either draw a graph with the given specifications or explain why no such graph exists. #18: tree, five vertices, total degree ...continues

Working with permutations and combinations

Permutations and coefficients (a) How many bit strings of length 7 are there? Explain. (b) How many bit strings of length 7 are there which begin with a 0 and end with a 1? Explain. (c) How many bit strings of length 7 is there that contain an even number of ones? Explain.