(a) List the ordered pairs that belong to the relation.

My ANS: (a,a),(b,a)(b,b),(c,a),(c,b),(c,c),(d,a),(d,b)(d,d)

(b) Find the (boolean) matrix of the relation.
< my answer file attached as Mr.jpg>

I did review another answer posted along the same question, but uses a different shape. I think my matrix is correct based on my pairs, but i'm concerned about the pairs.

Please provide some guidance on this exercise. The more I read about digraphs, closure of relations, and Hassediagrams the more confused I get. It is just not sinking in. Please help and explain this text exercise.

Let A = {a, b, c} and let R be the relation defined on A defined by the following matrix:
M=R = [1,0,0; 1,1,0; 0,1,1
(a) Describe R by listing the ordered pairs in R and draw the digraph of this relation.
(b) Is this relation a partial order? Explain. If this relation is a partial order, draw its Hasse diagram.

Please see the attached.
Consider the following Hasse diagram of a partial ordering relation R on a set A:
(a) List the ordered pairs that belong to the relation. Keep in mind that a Hasse diagram is a graph of a partial ordering relation so it satisfies the three properties listed in number 5 part(b).
(b) Find the (Boo

S = {0,1} and consider the partial order relation R defined on S X S X S as follows: for all ordered triples (a, b, c) and (d, e, f) in S X S X S.
( a, b, c ) R ( d, e, f ) <-> a ≤ d, b ≤ e, c ≤ f,
where ≤ denotes the usual "less than or equal to" relation for real numbers. Please demonstrate how to draw

Please see the attached file for the fully formatted problems.
Consider the following Hasse Diagram of a partial ordering relation R on a set A.
5
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Given S = {0, 1}, let R be the partial order relation on S X S X S such that for all ordered triples (a, b, c) and (d, e, f) in SXSXS (a, b, c) is related to (d, e, f) a =

Please see the attached file for the fully formatted problems.
Let A = {1, 2, 3, 4, 5, 6,12} and define the relation R on A by m R n iff
m|n.
Write the definitions of the properties, reflexive, antisymmetric and transitive and the use
the definitions to determine whether each property holds for this relation.
(a) Is thi

Qu1) Is it true that ρ(AUB)= ρ(A) U ρ(B)? justify your answer.
Qu2) Consider the function f:A→A defined by f(x)=x+1 and justify your answers.
a) For A=ν (integers) is f onto?
b) For A=R(real number) is f injective?
c) For A=Q (rationals) is f onto?
d) For A=Z(all integers) is f a bijection?
Q3)
a) Let f : R→R

A set S of jobs can be ordered by writing x ≤ y to mean that either x = y or x must be done before y, for all x and y in S. The following is a Hasse diagram for this relation for a particular set S of jobs:
(see attached)
a. If one person is to perform all the jobs, one after another, find an order in which the jobs