**Learning Goal: **I’m working on a computer science question and need the explanation and answer to help me learn.

I have five questions I need an answer for please

1) Define a relation S from R to R as follows:

For all (x, y) R R,

(x, y) S means that x y.

a. Is (2, 1) S? Is (2, 2) S? Is 2 S 3? Is (1) S (2)?

b. Draw the graph of S in the Cartesian plane.

2) Let A = {4, 5, 6} and B = {5, 6, 7} and define relations R, S, and T

from A to B as follows:

For all (x, y) A B,

(x, y) R means that x y.

(x, y) S means that

2 is an integer.

T = {(4, 7), (6, 5), (6, 7)}.

a. Draw arrow diagrams for R, S, and T .

b. Indicate whether any of the relations R, S, and T are functions.

4) Let A = {1, 0, 1} and B = {t, u, v, w}. Define a function

F: A B by the following arrow diagram:

a. Write the domain and co–domain of F.

b. Find F(1), F(0), and F(1).