Question

Let S be the set of all subsets of Z. Define a relation,∼, on S by “two subsets A and B of Z are equivalent,A∼B, if A⊆B.” Prove or disprove each of the following statements:

(a)∼is reflexive(b)∼is symmetric(c)∼is transitive

Answer 1

ons by # Lets be the set of all subsets of z. Define a relation Two subsets A and B are Equivalent, Au. ß ACB prove of disprove Each of the following statemente is reflexive © is symmetric On is transitive @ s = Set of solution Given - All subset of z szę A ; ASZ? define relation in . Two subsets A and B are Equivalent ů. ACB @ Reflexive : از سر مزار

- V AC Z then AC since. Every set is subset of gtself. is reflexive. 6 u Example Symmetrics is net symmetric A = { 1, 2, 2}: B={1,2,3,4,5) A CB e A is subset of B Let B then

But, here п£А ie B is not subset of A Неиск relation a is most symmebic. BE у © Transitive: is transitive because M UR, у А, В, cz 4 П» + Аср , Вс сэдс с aika Hut 4 As f ( 2 ) ( 1 2 3 } c: fi, 2, 34) Нек. АСВ, ВСС ЭАСС So in is transitive ů is net symmetric hence Vis jwjh2Јh il. фр 24 Wik2]h w pВ 22ң is het Equivalene Relation. since л