Answer to Question #26097 in Discrete Mathematics for Venzo

Question

Let relation defined as below:

(i) Write R1 relation as a set of ordered pairs. Draw the arrow diagram and determine whether R1 is a function or not. Explain your answer.
(ii) Hence, determine whether the R1 relation is an equivalence relation or a partial order (or neither).

(iii) Describe how the digraph of the R1 relation be used to determine whether R1 is an equivalence relation. Your answer should include the digraph and detailed description.

(iv) Determine the matrix of the R1 relation (relative to the given orderings). Now, reorder R1 as 3,2,1,4, and determine the new matrix obtained.

(v) Another technique to test for reflexive, symmetric and transitivity is by using the
matrix of relation. Analyze matrix of the R1 relation to determine whether it is an
equivalence relation.