discrete mathematics?

[Aya AuRoRa]

Relation R1 is defined below:
R1 = {(p,q) | p-q is even}; R1 on set M = {1,2,3,4};
Ordering of M: 1,2,3,4
a) Write the relation R1 as a set of ordered pairs. Draw the arrow diagram and
determine whether R1 are functions or not. Explain your answer.
b) Hence, determine whether the relation R1 is an equivalence relation or partial order
(or neither both).
c) Describe how can the digraph of the relation R1 be used to determine whether R1 is
an equivalence relation. Your answer should include the digraph and detail
description.
d) Determine the matrix of the relation R1 (relative to the given orderings). Now,
reorder R1 as 3,2,1,4, thus determine the new matrix obtained.
e) Another technique to test for reflexive, symmetric and transitivity is by using the
matrix of relation. Analyze matrix of the relation R1 to determine whether R1 is
an equivalence relation.
Another property of relation is irreflexive which is defined as follow:
A relation R on set N is irreflexive if for every x Î X, (x,x) Ï R. That is, R is irreflexive if
no element in N is related to itself.
e) Determine whether R1 is irreflexive.
f) Explain the difference between irreflexive and reflexive.

[DC - ??]

R1 on set M = {(1,1) , (1,3) , (2,2) , (2,4) , (3,1) , (3,3) , (4,2) , (4,4)}

you can start with that one... and find out the rest... they are not that complicated...


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