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For all real numbers a and b, where , let .  Then which of the following ... ...

   For all real numbers a and b, where , let .  Then which of the following must be true?   I.  a◊b = b◊a II.  a◊a = (a + 1)(a – 1) III.  (a◊b)◊c = a◊(b◊c)
(A) I only
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Press: Set D - Defined functions

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Replies to This Thread: 1 | ----
For all real numbers a and b, where , let .  Then which of the following ... ... 
Posted: 01/29/2014 19:21
Why can't a and b both be equal to 1. This would make I true and it still works with the original "a times b doesn't equal zero". I felt that the question needs to say a doesn't equal b.
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Posted: 01/31/2014 10:42
Tyler, your example would make I true only for that particular example. We need I to be true for "all real numbers", where a and b are not 0.
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