   SEARCH HOME Math Central Quandaries & Queries  Question from Nazrul, a teacher: Given that A={-2,-1,0,1,2}, S={(x,y): x belongs to A, y belongs to A and y^2=x}. How can I find the domain and range of the relation S. What is the inverse relation of S. Please show me the process in details. Thank you. Nazrul,

Let me solve this problem:

Given that B={-4,-2,0,4}, S={(x,y): x belongs to B, y belongs to B and y2=x}. Find the domain and range of the relation S. What is the inverse relation of S.

The key here is that x and y are in B and x is the square of y. Go through the elements of B, square each and see if the result is in B.

(-4)2 = 16: Not in B
(-2)2 = 4: In B
02 = 0: In B
42 = 16: Not in B

Since (-2)2 = 4, (4,-2) is in S.
Since 02 = 0, (0,0) is in S.

Thus S = {(4,-2), (0,0)}.

The domain of a relation is the set of all first coordinates and hence the domain of S is {4, 0}. The range of a relation is all the second coordinates and hence the range of S is {-2, 0}. To construct the inverse of S replace each element (x,y) in S by (y,x). Thus the inverse of S is {(-2,4), (0,0)}.

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.