YouLetRbetherelationonN definedbyR=(x,y)|x3y12i) Write R as a set of ordered pairs.ii) Find R1iii) Find the domain and range of R

i) To write R as a set of ordered pairs, we need to find all the natural number solutions (x, y) to the equation x + 3y = 12. The natural numbers are the set of positive integers, including zero. So, we can start by setting y = 0, 1, 2, 3, 4 and solve for x each time. We get the following pairs: (12,0), (9,1), (6,2), (3,3), (0,4). So, R = {(12,0), (9,1), (6,2), (3,3), (0,4)}.

ii) The inverse of a relation R, denoted as R^-1, is the set of ordered pairs obtained by swapping the elements in each pair from R. So, R^-1 = {(0,12), (1,9), (2,6), (3,3), (4,0)}.

iii) The domain of a relation is the set of all first elements (x-values) in the ordered pairs. So, the domain of R is {0, 3, 6, 9, 12}. The range of a relation is the set of all second elements (y-values) in the ordered pairs. So, the range of R is {0, 1, 2, 3, 4}.