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.

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.

Show that the relation R is 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 equivalence classes of 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.

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.

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 equivalence classes of R .

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} 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 on the set A={x in Z ;0lt=xlt=12} , given by R={(a ,\ b): a=b} , is an equivalence relation. Find the set of all elements related to 1.

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