If `R={(1,2),(2,3)}` is a relation in N, list the least number of ordered pairs to be included in R so that R is an equivalence relation.

A binary relation R in the set A={2,3,4,5,6} is defined by xRy, where |x-y| is divisible by 3. Is R an equivalence relation?

Let N be the set of all natural numbers and R be the relation in NxxN defined by (a,b) R (c,d), if ad=bc. Show that R is an equivalence relation.

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} .

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 ?

Let L be the set of all lines in the XY - plane and R be the relation in L defined by R={(l_(i)l_(j))|l_(i)" is parallel to "l_(j)l_(i)AA_(i),j} . Show that R is an equivalence relation. Find the set of all lines related to the line y=7x+5

State true or false: R= {(a,b) : a,b in N , a+b>0} is an universal relation in N.

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?