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 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 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 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 R in the set R of Real numbers defined as R={(a,b):aleb^2} is neither reflexive, nor symmetric, nor transitive.

Consider the relation in the set N of natural numbers defined as R={(a,b):ab is a factor of 6}. Determine whether the relation is reflexive, symmetric or transitive.

If R is a relation on the set N of natural numbers defined by a+3b=12 .Find R.

If R is a relation on the set N of natural numbers defined by a+3b=12 .Find range of R.

If R is a relation on the set N of natural numbers defined by a+3b=12 .Find domain of R.

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}.