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!