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.

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 a relation in T given by R={(T_1,T_2): T_1~=T_2} . Show that R is an equivalence relation.

Let R be a relation on the set of all line in a plane defined by (l_1, l_2) in R iff l_1 is parallel to line l_2dot Show that R is an equivalence relation.

Let R be a relation on the set of all lines in a plane defined by (l_1,\ l_2) in R line l_1 is parallel to line l_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 with sides 5,\ 12 ,\ 13 and T_3 with sides 6, 8, 10. Which triangles among T_1,\ T_2 and T_3 are related?

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.

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

If R_1 and R_2 are equivalence relations in a set A, show that R_1nnR_2 is also an equivalence relation.

If R_1 and R_2 are equivalence relations in a set A, show that R_1nnR_2 is also an equivalence relation.

Show that the relation R defined in the set A of all triangles as R={(T_1,T_2): T_1( i s s i m i l a r t o T)_2} , is equivalence relation. Consider three right angle triangles T_1 with sides 3, 4, 5, T_2 with sides 5, 12, 13 and T_3 w