Question

m) Recall z = { 07, s... al. (200) anabelian group and (2010) isa Semigroup with identity [1] Let A- 41],3], [-],[9]} B-{{], [2], [4][5][6], and oil is a commutative Ist a binary operation on A? Give reasons it is, write out its multiplication table. 2) is a binary operation on B? Give Resisons! If it is, write out its multiplication table. 3 25 is a binary operation on A? f it is, write out its multiplication Give reasons. table. 4) Is i a binary operation on B? If yes, write out multiplication Give Reasons. tabl. 5) Find a subset C of 8 such that Ic/=2 and cc, io) is a group. write out table 6) Find a subset D of B such that pl =4 and coi ) is a group, write out table

Answer 1

1. No. Becausou [194 [3] + [1] 4^' 2. No. Becalvo (111151199 / B ·10 131 111111 D'1 [11 137 13 191 (31/ [3] [9] [1 11 3. Yes . 1971/197171 [3] [1] WA. I rol [ 21 111 1s] [187 | | | | | [] [*] [*] [*] 121) [] [1] [8] [o] [?] [6] 11] ] [8] [6] [O] [1] [2] (5) 107 107 ('T [ ] LOJ LOJ [6] [] [2] [1] [] 15T [8] [8] o [6] [?] [] [8] [1] . for au 3 , 4 , 8 , :1 ( 8 . so it is binary operation, } in group under 10. 5. P={A], T 191 6. Ouerto identity ( 10 117 kg (4) ( . 9.95 $21,61,6[4]} auare (CJ aormenting