Show that the relation R defined in the set A of all polygons are as `R = {(P_1,P_2) : P_1, P_2 in A}` `P_1 and P_2` have same number of sides is an equivalence relation. What is the set of elements in A which are related to the rectangle having sides 4 and 5 cm?

Let L be the set of all straight lines in the XY plane and let R be a relation defined in L as R={(L_1,L_2) : L_1, L_2 in L} L_1 is parallel to L_2 Show that R is an equivalence relation. What is the set of lines related to the line y=2x+3 ?

Is the relation R={(L_1, L_2) : L_1,L_2 in L} and L_1 is perpendicular on L_2 an equivalence relation in the set L of all straight lines in the coordinate plane?

Show that the relation R in the set of integers given by R={(a,b):4" divides "a-b} is an equivelence relation. Find the set of all elements related to 0.

Show that the relation R in the set Z of integers given by R{(x,y):6" divides "x-y} is an equivalence relation. Find the set of all elements related to 0.

Show that the relation R in the set A={x in Z:0lexle12} given by R={(a,b):|a-b|" is multiple of "4} is a equivalence relation. Find the set of all elements related to 1.

Let R be the relation defined in the set A={1,2,3,4,5,6,7,8,9} by R={(a,b,):" both a and b are either odd or even"} . Show that R is an equivalence relation. Further show that all the lements of the subset {1,3,5,7,9} are related to one another and all the lement of the subset {2,4,6,8} are related to one another but no element of the subset {1,3,5,7,9} is related to any element of the subset {2,4,6,8} .

Define a relation in the set A={1,2,3,4} which is transitive but not symmetric.