Let T be the set of all triangles in a plane with R a relation in T given by `R={(T_1,T_2): T_1" is congruent to "T_2}`. Show that R is an equivalence relation.

Let T be the set of all triangles in a plane with R as relation in T given by R={(T_(1),T_(2)):T_(1)~=T_(2)}. Show that R is an equivalence relation.

Show that the relation R defined on the set A of all triangles in a plane as R={(T_(1),T_(2)):T_(1) is similar to T_(2) ) is an equivalence relation.Consider three right angle triangle T_(1) with sides 3,4,5;T_(2),10. sides 5,12,13 and T_(3) with sides 6,8,10. Which triangles among T_(1),T_(2) and T_(3) are related?

Let A be the set of all triangles in a plane show that the relation R={(Delta_(1),Delta_(2)):Delta_(1)~Delta_(2)} is an equivalence relation on A .

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as a\ R\ b if a is congruent to b for all a ,\ b in T . Then, R is (a) reflexive but not symmetric (b) transitive but not symmetric (c) equivalence (d) none of these

Show that the relation R defined in the set A of all triangles as R={(T_(1),T_(2)):T_(1) is similar to T_(2) }, is equivalence relation.

Show that the relation is congruent to on the set of all triangles in a plane is an equivalence relation

Let R be the real line. Consider the following subsets of the plane RxxR . S""=""{(x ,""y)"":""y""=""x""+""1""a n d""0""<""x""<""2},""T""=""{(x ,""y)"":""x-y"" is an integer }. Which one of the following is true? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not