Question

Let X, be the set {x € Z|3 SXS 9} and relation M on Xz defined by: xMy – 31(x - y). (Note: Unless you are explaining “Why not,” explanations are not required.) a. Draw the directed graph of M. b. Is M reflexive? If not, why not? C. Is M symmetric? If not, why not? d. Is M antisymmetric? If not, why not? e. Is M transitive? If not, why not? f. Is M an equivalence relation, partial order relation, neither, or both? g. If M is an equivalence relation, what are the equivalence classes of M? (else write "n/a".)

Answer 1

3- {net | 32 x 2 ay - 3,4,5,6,7,8,9) on X₂ a My => 3 1 (nry) (Me Xzxxz) defined by M is a relation ca. ebr 75 85 95 Directed graph off M (6) Mis reflexive holds a Ma a & V rEXz 31(0-2) =0 Vw EXg (e.) M is symmetric het, xMy hold ny EX3 >) 31 A-4 =) 31 -Cara) holds. =) 31 (y-2) =) yma (d) M is NOT antisymmetric 3M 6 holds 6 M 3 also holts but 3+ 6 - (e) Mis tramitive any and yMz hold 2,y,z EX, >) 316-y] and 3)(y-2) => 3)(n+y)+(012) -) 3 | n-2 =) xMz holt. It.) M is an equivalence het . relation on X3 . (9) ane [3] = equivalence class of 3 {3, 6, 93 [4] = { 17), [5] = { 5.8) where, Ease { b Exz | 31 (9-b)] for a FX3.