I want to write clear Let 5 123 12 and T 123 30 Define the

I want to write clear

Let 5 = {1,2,3, ,12} and T = {1,2,3, ,30}. Define the relations R on S and T by (s, t) R t = 3s - 1. List the elements R and domain and range of R. Let A = {2,4} and B = {6,8,10} and define the relations R and S from A to B as follows: (x,y) R x|y. (x, y) S y - 4 = x. List the elements of A Times B, R, S, R S, and R S. Let be the relation on the real numbers given by xRy iff |x - y| LE 2. Prove that this relation is Reflexive, Symmetric but not transitive. Let S = lxl and define a relation on S by (a, b),(c,d) if d-b= 4(c - a). Show that ~ is an equivalence relation. Define a relation on R by, x- y if x - y is rational. Prove that is an equivalence relation.

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