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Question: Consider the relation R on A defined by aRb iff 1mod4 = bmod4 a)Construct the...

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

Solutions

Expert Solution

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:

Colby Messinger answered 1 year ago

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