Let G be a set of rational numbers other than 1. Let * be an operation on G defined by a*b=a + b + ab for all a, b € G. Prove that {G, *} is a group. -

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 8 Marks

Year: May 2015

1. CLOSOURE

   Let A and B be elements of real numbers R. Then

   a * b=a + b + ab is also real. So it is in R.

2. ASSOCIATIVE

   a * (b * c)=a * {b+c+bc)=a+b+c+bc+ab+ac+abc

   (a * b) * c=(a+b+ab) * c=a+b+ab+c+ac+bc+abc=a * (b * c)

3. IDENTITY ELEMENT

   LET a …