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 4? Is 4 S 3? Is (4, 4)  S? Is (3, 2)  S? b. Write S as a set of ordered pairs. 5. The congruence modulo 3 relation, T, is defined from Z to Z as follows: for all integers m and n, m T n  3 | (m - n). (Yes/No answers sufficient; explanation optional) a. Is 10 T 1? Is 1 T 10? Is (2, 2)  T? ... click for more

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 symmetric d. determine whether the relation is transitive Give a counterexample in each case in which the relation does not satisfy one of the properties. 2. R2 = {(0,0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} 16. Determine whether or not the given binary relation is reflexive, symmetric, transitive, or none of these. Justify your answers. F is the congruence modul... click for more

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 10

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.