Question

3. For each of the relations below, draw their graph, and say which of the following properties they satisfy. Answer this question using the following sets. A = {0,1,2), B = {0}, D = P({0,1)) a. R= {(x,y) E AXA X Sy?) List of properties satisfied: b. R = {(x,y) EB X Bl x*y> 4} List of properties satisfied: Properties • Reflexive Anti-reflexive • Symmetric Anti-Symmetric Transitive Partial Order Total • Equivalence c. R= {(x,y) EDx D x A y = {0,1}} List of properties satisfied: d. R = {(x,y) E D x D x y = {0,1}} List of properties satisfied: e. R=BXB List of properties satisfied:

Thank You.

Answer 1

Give See A A= 50,1,2} B=0} D = Pleo) Do$0}, {}, {0,11%} @ R= {(,y) € Axala zy?] => 0, 0) (0) (0,2),(,1),(0,29 0,0) Sunce (010) (1,1) (2, 2) ER Ris Reflexive since (6) ER Bul (10) ER = R is not symmetric → Ris not Symmetric , R is anot Eduivalore. (2,4) ER, ALY V (84) ER =) Ris partial ordered =) Ris Partial ordered - Rºs lantisymmetric Since R S Reflaive , Antisymmetrie, transline.com Partial ordered 33 Ras frotal ordered Q R=Slay)E AXDAY Sols] R - Startte BxD) stay story R = {{0},{:})? R is not Reflerine ((22) ERFRED) Ris not Symmetric [ {}, {} ER Bul({1} {a} ) FR

R is Antireflexive (2, 4)ER X XEB Ris transitive trivially Ris And symmetric trivially Ris not partially ordered Ris not Total ordered b y Rů not Edenvale Ri. not symmetic 7 R = {(ay) & BXB 1 x *9>4} R is not reflexive, Ris only refienive Ris symmetric R is antisymmetric Ris transitive R is partial, R is not tolus. Ę not Execivelence

O R=SQUEDXDXCY=0,} 1 @ R = BXB RSCHE TA D/603,8,1], R=$(0,0% (89,80;})}{{1},80) Restolecki Res not reflewive Ris reflexive, and not anti-reflexive 0.0ER Ris gymmetric Ris not symmetric I Ris Anti Symmetric 1 RB not partial and not . toful RP. Eduivalence 8 transitive A 8, 2013 ER {{0,1} (47ER - Ris not antisymmetric [{ai} {1};) ER Res fansitive and Antisymmetrical and partial order and not tohul Ris not Eduivalence