Question

Hw 1 (I) For each of the following determine it 3 binary operation on A. Give Reasons. 1 A = {1, 2, 3, 2, -45 a*b=161 2) A = { 1, 6, 3, 2, 18} a*b = ab too 3) A = Z-sold a*b=ab 4) A = Q a*b=2a.b

Answer 1

The binary opefationo funciono fromAxA to A The birony operation AxA -J A A1,-2 ,3,2,-4 akb blis not C1,) 1 = nonempty set A On a are (T) C binary opefaton 111 =E A C-2.-2)-21= 2EA but (-u)=1-41 44A C2) A 1,6,3,2, 1 abab binany operation IS not a on A We note that 6,2 EA but 6*2- 12 A binay operaton Tharepre, is not a A 2-104 2-io) ab ab -432,, 1,2,3, 4,5.. C3) CSFS)(-E5) Here -31252 bialy opeah Heno, is not a

4A Q The et o atnalo. AGE ATE a b 2. not binary operation is o, 4글)드글초블드 2 S Since, a,b akbe 2 -4,-3,-2,-1 2 3hrth irrational numbar an