Show that the relation `R` on the set `Z` of integers, given by `R={(a ,\ b):2` divides `a-b}` , is an equivalence 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}.

Show that the relation R in the set is given by A={x in Z,0lexle12} R={(a,b):a-b is a multiple of 4} 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 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 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.

Let R be a relation on the set of integers given by aRb hArr a=2^(k)*b for some integer k. Then R is : a)An equivalence relation b)reflexive but not symmetric c)reflexive and transitive but not symmetric d)reflexive and symmetric but not transitive

Show that the relation R on the set N xx N defined by (a, b)R(c, d) iff a d(b+c)=b c(a+d) is an equivalence relation.

Let R be the relation on the set N of natural numbers given by R={(a,b):a-b>2b>3} Choose the correct answer

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.