If `R={(x, y): x +2y =8}` is a relation on N, then write the range of R.

If R = {(x, y): x + 2y = 8) is a relation on a set of natural numbers (N), then write the domain, range and codomain of R.

A R is a relation on set A such that R=R^(-1) , then write the type of the relation R.

Let. X = {1, 2, 3, 4, 5, 6, 7, 8,9}. Let R_(1) , be a relation on X given by R_(1) ={(x, y): x - y is divisible by 3)} and R_(2) , be another relation on X given by R_(2) ={(x, y): {x,y) sub (1,4,7) or (x, y) sub (2,5,8) or (x, y) sub (3, 6, 9)}. Show that R_(1)=R_(2) .

Let R be a relation defined on the set of natural numbers N as follows: R = {(x,y): x in N,y in N and 2x + y = 24). Then, find the domain and range of the relation R. Also, find whether R is an equivalence relation or not.

Show that the operation * given by x*y=x+y+ -xy is a binary oeration on Z,Q and R but not on N.

If R={(a, a^(3)) : a is prime number less than 5} be a relation. Find the range of R.

Check whether the relation R defined in the set A = {1,2,3,...,13,14 as R = {(x,y):3x - y =0} is reflexive, symmetric and transitive.

Let R={(a, a^(3)) : a is a prime number less than 5) be a relation. Find the range of R.