# Math (Discrete Mathematic)

1. Nov 2, 2009

### Yusuke_Ichigo

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.

I only understand this R1 on set M = {(1,1) , (1,3) , (2,2) , (2,4) , (3,1) , (3,3) , (4,2) , (4,4)}. Can anyone help?
Thank you.