LotX = {1,2,3,4}, and consider binary relations R and S, both subsets of X X X, defined i defined as follows. (i) R = {(1,1), (1,2), (2,1), (2,2), (4,1)} and (ii) S = Ā N{(i, i)|i € X} 1. Precisely list the elements of R-1. Is R a function from X to X (Yes/No and Justify)? How many elements does S x R contain? (Equivalently, find |S X R.) Hustify your answer.)

Consider the relations R = {(1,5), (2, 2), (3, 4), (5, 2)}, S = {(2,4), (3, 4), (3, 1), (5, 5)}, T = {(1,4), (3, 5), (4, 1)} on the set A = {1,2,3, 4, 5}. Find (a) SoR = (b) RoT = (c) ToS = (d) Ro R= (e) SoS = (() ТоТ%—

= {(1,2), (2,1), (1,1), (2,2), (3,3), (4,1)} Draw the directed graph of the relation R X= {1,2,3,4}.

Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric, antisymmetric, or transitive.

Let A={1,2,3,4} and let R be the relation from A to A R={(1,1),(1,4),(2,1),(2,2),(2,3),(3,1),(3,4),(4,3)} Create thr diagraph and matrix Mr for the relation

What is the kernel and image of the map

There are 16 binary relations on the set {0, 1}: (a) { } (d) {(1,0)} (g) {(0, 0), (1, 0)} (j) {(0, 1), (1, 1)} (m) {(0,0), (0, 1), (1, 1)} (b) {(0, 0)} (e) {(1, 1)} (h) {(0, 0), (1, 1)} (k) {(1, 0), (1, 1)} (c) {(0, 1)} (f) {(0, 0), (0, 1)} (i) {(0, 1), (1,0)} (1) {(0,0), (0, 1), (1, 0)} (0) {(0, 1), (1, 0), (1, 1)} (n) {(0,0), (1,0), (1, 1)} (p) {(0, 0), (0, 1), (1, 0), (1, 1)} For a-f use the letters for each relation above. a. List the reflexive relations on the set {0, 1}. b. List the irreflexive relations on the set {0, 1}. c. List the symmetric relations on the set {0, 1}. d. List the transitive relations on the set {0, 1}. e. List the antisymmetric relations on the set {0, 1}. f. List the asymmetric relations on the set {0, 1}.

Please just answer parts iv. and v.

Represent the relations on {1, 2, 3, 4} with a matrix and digraphs.  (The rows and columns correspond to the integers listed in increasing order). {(1, 1), (1, 4), (2, 2), (2, 3), (3, 1), (3. 2), (4, 2), (4, 3)}

Compute the complement of relation R. R={(1, 1), (5, 1), (5, 5), (6, 1), (6, 6), (7, 1), (7, 7)}