Show that the relation `R` , defined on the set `A` of all polygons as `R={(P_1,\ P_2): P_1` and `P_2` have same number of sides}, is an equivalence relation. What is the set of all elements in `A` related to the right angle triangle `T` with sides 3, 4 and 5?

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have same number of pages} is an equivalence relation.

Show that the relation R on the set A of all the books in a library of a college given by R={(x ,\ y): x and y have the same number of pages}, is an equivalence relation.

If R is an equivalence relation on a set A, then R^-1 is

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 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 on the set A={x in Z :0lt=xlt=12} , given by R={(a ,\ b):|a-b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1 i.e. equivalence class [1].

Show that each of the relation R in the set A={x in Z :0lt=xlt=12} , given by(i) R = {(a , b) : |a - b| is a multiple of 4} (ii) R = {(a , b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.

Show that the relation S in the set A={x\ \ Z\ :0\ lt=x\ lt=12} given by S={(a , b):\ a ,\ b\ \ Z ,\ \ |a-b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1.

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

Show that the relation R on the set A{xZ ;0lt=12}, given by R={(a , b): a=b}, is an equivalence relation. Find the set of all elements related to 1.