Question

(1) For each of the following relations on R, is the relation reflexive? Is it symmetric? Is it transitive?

(a)r1={(x, y)∈ R × R | xy= 0}

(b) r2={(x, y)∈R×R|x2+y2= 1}

(c)r3={(x, y)∈R×R||x−y|<5}

Answer 1

7 riding, ERX RI nyo} since (oo) Eri Let 2 ER Siti a to 3 de d = 2 2 2 7 Kia) & ri s cia

I The relation in dit is not as identity relation does not reflenine. hold in a (mygt i sit ny=b a n-ö on yo => Ynzo & Gint n, if Ingler => riplation in ri is symmetric

0 then [li] & ng = 1, 4 ho+ +7 он м . + Let me = L ay FIRAR 1 ? ty? - 1} clearly ill fra су ? +*2 г - Хит 2 - 2 ) н а ( 11 )) +. - ² the relation na is het С (и, сера. 3. 2. и* e- N2 и 5*) - Эъчи” – - Сли), . If (il fro then (y,x) E na is symmetric i let Clios , cuj & then 1260 ? = 1 A -- о: #1 - ) , 34 - 1 4 1 2 4 . Я. (1.1). ¢ - - trg is het transitive Е

0 then [li] & ng = 1, 4 ho+ +7 он м . + Let me = L ay FIRAR 1 ? ty? - 1} clearly ill fra су ? +*2 г - Хит 2 - 2 ) н а ( 11 )) +. - ² the relation na is het С (и, сера. 3. 2. и* e- N2 и 5*) - Эъчи” – - Сли), . If (il fro then (y,x) E na is symmetric i let Clios , cuj & then 1260 ? = 1 A -- о: #1 - ) , 34 - 1 4 1 2 4 . Я. (1.1). ¢ - - trg is het transitive Е

© + 3 смy) E12 <1 1 1-9) « Гу let (0, 1) ERTIR - Sina . o o — 1) - 12г а (о, 1), е на а та Ер. let nEIR CanJE IRXIR. Ә) « — к] =2 Г =) (+ ри) - @ ата - і ---- Lжу, Let (noltro. а) - 1 - 94 Г. А 9-х) с -=- Суучу ета. ng is symmetric Дуо и (ис (9, yeni - 2 х =7/ г сы-19-) :: 21 и-Уty- г) ------ [х гурғу, - L er ) к. 1 Ір. r3 is not transitive