Prove that ,the relation R on the set A={1,2,3,4,5,6,7,8,9,10,11,12,13} defined by aRb if and only if a-b is divisible by 3 ,is an equivalence relation.

Prove that the relation R is the set A= {5,6,7,8,9,10} given by R= {(a, b) : |a - b| is divisible by 2} is an equivalence relation. Find the all elements related to the element 6.

Prove that the relation R in the set A={5,6,7,8,9} given by R={(a,b):|a-b|, is divisible by 2}, is an equivalence relation.Find all elements related to the element 6.

Is the relation R in the set A={1,2,3,4,5} defined as R={(a,b):b=a+1} reflexive ?

If R is a relation on the set A={1,2,3,4,5,6,7,8,9} given by xRyy=3x then R=

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b):|a b | is divisible by 2} is an equivalence relation.Write all the quivalence classes of R .

Show that the relation R in the set A = {1, 2, 3, 4, 5,6,7} given by R = {(a , b) : |a - b| " is even" } , is an equivalence relation.

Prove that the relation R in the set A={1,2,3,4,5,6,7} given by R={(a,b):|a-b|iseven} is an equivalence relation.

Show that the relation R defined by R={(a,b):a-b is divisible by 3;a,b in Z} is an equivalence relation.

Prove that the relation R on Z defined by (a,b)in R hArr a-b is divisible by 5 is an equivalence relation on Z .

Let R be the relation defined on the set A={1, 2, 3, 4, 5, 6, 7} 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 elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.