Consider the following relation R on the set of all teachers in RU. Teacher1 is

Question

Consider the following relation R on the set of all teachers in RU. Teacher1 is

related to Teacher2 if and only if Teacher1 and Teacher2 were active in the

Kitchenware revolution. Show arguments to determine the answers to the following

questions.

a)  Determine whether the relation is reflexive. Provide arguments.

b)  Determine whether the relation is symmetric. Provide arguments.

c) Determine whether the relation is transitive. Provide arguments.

d)  Determine whether the relation is an equivalence relation and if so describe

the equivalence classes.

Explanation / Answer

to show relation is reflexive

=> we have to show teacher1 is related to herself!

=> if teacher 1 is active then teacher 1 is realted to herself because teacher 1 is active.

so relation is reflexive.

2)now if teacher1 is related to teacher 2 => teacher 1 and teacher 2 are active.

so if teacher 2 is related to teacher 1 condition required is teacher 2 and teacher 1 should be active. which is granted .

so teacher 2 is related to teacher 1.

so relation is symmetric.

3) now if teacher 1 is related to teacher 2 => teahcer 1 and 2 are active.

if teacher 2 and teacher 3 are related.=> teacher 2 and 3 are active.

no both teacher 1 and teacher 3 are active.

so teacher 1 is related to teacher3

so relation is transitive.

since the relation is relfexive symmetric and transitive so the relation is and equivalence relation.

and the equivalence class is all the teachers who are active in kitchenware revolution. i.e among all the teachers the subset of teachers who are active is an equivalence class.

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