In: Advanced Math
Question: Consider the relation R on A defined by aRb iff 1mod4 = bmod4
a)Construct the diagraph for this relation
b)show that R is an equivalence relation
Part B: Now consider the relation R on A defined by aRb iff a divides b (Divides relation)
c) Show that R is partial ordering
d) Contruct the hasse diagram for this relation
Part-A:
The relation is
(i)Reflexive
since
(ii):Symmetric
Suppose that
Hence
(iii):Transitive
Suppose that
Hence
Again
Suppose that
Hence
Thus we have
Hence
From (i),(ii),(iii) R is equivalence relation
If we consider the vertices as
then using above we find that
Prt-B:
(I) Reflexive since
(II) Anti-Symmetric since
(III)Transitive since
Hence equivalence
Hasse Diagram:
Consider the set with the above relation: