Show that each of the relation R in the set A={x in Z: 0 le xle12} ,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 in each case.

Show that the relation 'S' in set A={x inz:0lexle12} given by S={(a,b):a.bin z,|a-b| is divisble by a} is an equivalence relation.

Show that the relation R on the set of natural numbers defined as R:{(x,y):y-x is a multiple of 2} is an equivalance relation

Show that each of the relation R in 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 in each case.

Show that the relation R in the set A = (1,2,3,4,5} given by R = {(a,b) : |a - b| is even }, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1, 3, 5} is related to any element of {2,4}.

The relation R defined in the set A={-1,0,1} as R={(a,b):a=b^2} Is R an equivalance relation

When a relation R on a set A is said to be reflexive

Let f: X rarr Y , be a function. Define a relation R in X given by: R={(a, b): f(a)=f(b)} Examine if R is an equivalence relation.

Show that the relation R in the set R of real number, defined as R = {(a.b): a lt= b^2} is neither reflexive nor symmetric nor transitive.

Show that the relation R in the set {1,2,3} given by R ={(1,2),(2,1 )} is symmetric but neither reflexive nor transitive