Homework help----proof

[May Day]

3.6 (Courtesy of J. Lagarias.) Let S be any set with at least two elements. Define a product on S by setting
ab = b for every a,b belong to S.
(a) Prove that S is closed under this product, that associativity holds, and that one can get from any element
of S to any other via the product.
(b) Explain why S is not a group.


hope someone can prove it
thank you guys in advance

 

[Mrspi]

3.6 (Courtesy of J. Lagarias.) Let S be any set with at least two elements. Define a product on S by setting
ab = b for every a,b belong to S.
(a) Prove that S is closed under this product, that associativity holds, and that one can get from any element
of S to any other via the product.
(b) Explain why S is not a group.


hope someone can prove it
thank you guys in advance

I can prove it...but I'm not going to do the work for you.

Parts of this are VERY easy to prove...closure and associativity, for example.

If you're in a class dealing with this kind of problem, I would expect to see some effort on your part. Show us what you've tried, and we'll go from there.