Question

Show that a*b = a+ab is binary associative

Answer 1

Answer:

For the binary operation, you need to prove that a∗b≠−1 iff a, b≠−1, that is

a∗b+1=a+b+ab+1≠0.

For identity, you want an e with a∗e=e∗a=a. As ∗ is commutative, all one needs is that a∗e=a, that is

a+e+ae=a.

Can you solve that for e in terms of a? And is the result independent of a?

Once you have done that, do inverses. You then need to solve a∗b=e for b in terms of a, that is

a+b+ab=e

where you now know e.

Please mark as brainliest answer if it helps.

thanks