Originally Posted by

**dude15129** Hey, I am not entirely sure if I am doing this right. But anyways...

The directions say...

"Determine whether the binary operation * defined on the given set results in a group."

(A group is classified by 3 properties:

Associative Law a * (b * c) = (a * b) * c

Existence of an Identity: There exists an element, e, such that

a * e = e * a = a

Existence of Inverses: For each element, a, there exists an element, s,

such that a * s = s * a = e (the identity)

So, here is what I'm supposed to do:

(a) Let * be defined on the positive reals by a * b= √(ab)

(b) Let * be defined on all the Reals except 0, by a * b= a/b

(c) Let * be defined on all the Reals except 0, by a * b= a+b+ab

Any help would be much appreciated!