Discussion
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)
*This question is included in Nova Press: Set D - Defined functions, question #7
, 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) | ... |
| (F) | ... |
The solution is
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.
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.