题目信息
If 
denotes a mathematical operation, does x y = y x for all x and y ?
denotes a mathematical operation, does x y = y x for all x and y ?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Algebra Functions
For all x and y, x
y = 2(x2 + y2) is equal to y x = 2(y2 + x2); SUFFICIENT.
If x y = 2(x2 + y2) for all x and y, then 0 y = 2y2 for all y and x y = y x for all x and y. However, if x y = 2(x3 + y2) for all x and y, then 0 y = 2y 2 for all y, but 1 2 = 2(13) + 2(22) = 10 and 2 1 = 2(23) + 2(12) = 18; NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
For all x and y, x
y = 2(x2 + y2) is equal to y x = 2(y2 + x2); SUFFICIENT.
If x y = 2(x2 + y2) for all x and y, then 0 y = 2y2 for all y and x y = y x for all x and y. However, if x y = 2(x3 + y2) for all x and y, then 0 y = 2y 2 for all y, but 1 2 = 2(13) + 2(22) = 10 and 2 1 = 2(23) + 2(12) = 18; NOT sufficient.The correct answer is A;statement 1 alone is sufficient.
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