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