Question

In the following a set is given and a binary operation is defined on it.Find whether the binary operation is commitative or associative or both in.


=>Z:aob=a+b+ab for all that a,b belongs to Z.​

Answer 1

Answer:

Step-by-step explanation:

Hola!

Let a,b€ Z.

Now, aob=a+b+ab

= b+a+ba=boa.

Therefore, o is commutative in Z.

Let a,b,c€ Z.

Now,

(aob)oc=(a+b+ab)oc.

=a+b+ab+c+(a+b+ab)c

=a+(b+c+bc)+a(b+c+bc)

=ao(b+c+bc)

=ao(boc).

So that o is associative in Z.

it's true.

Thank you !

Answer 2

Answer:

Check the attachment :)