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I am trying to answer the question: On the set R-{-1} define the operations a⊕b=a+b+aba⊕b=a+b+ab and axb=0axb=0. Determine if (R - {-1}, ⊕, x) is a ring. Is it a commutative ring with unity?

However I have no idea what this set even is/looks like. Any help is greatly appreciated!

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This is R, the set of all real numbers with the set {-1} removed. That is, the set of all real numbers except -1.

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The notation $R-\{-1\}$ means the same thing as $R\setminus \{-1\}$. They both denote the set $\{x\in R\mid x\neq -1\}$.

(In general, $A - B$ and $A\setminus B$ are notations for the set $\{x\mid x\in A\text{ and }x\notin B\}$.)

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