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## Homework Statement

- For the following sets, with the given binary operation, determine whether or not it forms a group, by checking the group axioms.

## Homework Equations

- (R,◦), where x◦y=2xy+1

- (R*,◦), where x◦y=πxy and R* = R - {0}

## The Attempt at a Solution

For question 1, I found a G2 identity to be 1/2 - 1/(2x), meaning x cannot be zero and therefore (R,◦) is therefore not a group. Is this in the right ballpark?

For question 2, I found a G2 identity to be 1/π, and a G3 inverse to be 1/(π²

**x), (since x does not equal zero). G1 is closed and G4 is associative, so (R*,◦) is a group.**[/B]