- #1
rbzima
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Please HELP!
So, I have to go about proving the following, but I have no idea where to even start:
I. Let S = R – {3}. Define a*b = a + b – (ab)/3.
1. Show < S,*> is a binary operation [show closure].
2. Show < S,*> is a group.
3. Find *-inverse of 11/5
II. Let G be a group with x,y contained in G .
Prove: (xy)^2 = x^2 y^2 which implies xy = yx.
xy = yx which implies (xy)^2 = x^2 y^2.
III. Let G be a group with x • x = e , For any x contained in G.
Prove: G is an abelian group.
Honestly, any help would be great because I really have no idea where to even start for any of these!
P.S. - This is not homework, but simply review for a test coming up in Abstract Algebra.
So, I have to go about proving the following, but I have no idea where to even start:
I. Let S = R – {3}. Define a*b = a + b – (ab)/3.
1. Show < S,*> is a binary operation [show closure].
2. Show < S,*> is a group.
3. Find *-inverse of 11/5
II. Let G be a group with x,y contained in G .
Prove: (xy)^2 = x^2 y^2 which implies xy = yx.
xy = yx which implies (xy)^2 = x^2 y^2.
III. Let G be a group with x • x = e , For any x contained in G.
Prove: G is an abelian group.
Honestly, any help would be great because I really have no idea where to even start for any of these!
P.S. - This is not homework, but simply review for a test coming up in Abstract Algebra.
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