Answer :

It is given that the relation R defined in the set A of all polygons as

R = {(P1, P2): P1 and P2 have same number of sides},


Then, R is reflexive since (P1, P2) ϵ R as the same polygon has the same number of sides with itself.


Let (P1, P2) ϵ R


P1 and P2 have the same number of sides.


P2 and P1 have the same number of sides.


(P2, P1) ϵ R


Therefore, R is symmetric.


Now, let (P1, P2), (P2, P3) ϵ R


P1 and P2 have the same number of sides. Also, P2 and P3 have the same number of sides.


P1 and P3 have the same number of sides.


(P1, P3) ϵ R


Therefore, R is transitive.


Thus, R is an equivalence relation.


The elements in A related to the right-angled triangle (T) with sides 3, 4 and 5 are those polygons which have 3 sides.


Therefore, the set of all elements in A related to triangle T is the set of all triangels.


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