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Define x?y to be |x - y| for all real numbers x and y. Which of the fo

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Bunuel
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Define x?y to be |x - y| for all real numbers x and y. Which of the fo [#permalink] New post   19 Mar 2019, 02:07
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Define x?y to be |x - y| for all real numbers x and y. Which of the following statements is not true?


(A) x?y = y?x for all x and y

(B) 2(x?y) = (2x)?(2y) for all x and y

(C) x?0 = x for all x

(D) x?x = 0 for all x

(E) x?y > 0 if \(x \neq y\)
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C
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Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo [#permalink] New post   19 Mar 2019, 06:06
Bunuel wrote:
Define x?y to be |x - y| for all real numbers x and y. Which of the following statements is not true?


(A) x?y = y?x for all x and y

(B) 2(x?y) = (2x)?(2y) for all x and y

(C) x?0 = x for all x

(D) x?x = 0 for all x

(E) x?y > 0 if \(x \neq y\)


for x?0 = x for all x
0>x
not sufficient
IMO C
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Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo [#permalink] New post   19 Mar 2019, 11:56
Bunuel wrote:
Define x?y to be |x - y| for all real numbers x and y. Which of the following statements is not true?


(A) x?y = y?x for all x and y

(B) 2(x?y) = (2x)?(2y) for all x and y

(C) x?0 = x for all x

(D) x?x = 0 for all x

(E) x?y > 0 if \(x \neq y\)



Yes if X = -2 then x?y
|-2-0|=2 which is \(\neq\) -2
Hence C is not true .
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Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo [#permalink] New post   08 Dec 2020, 21:01
Substitute numbers in the range and we can setup this

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Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo [#permalink] New post   08 Dec 2020, 21:01
Substitute numbers in the range and we can setup this

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Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo [#permalink] New post   08 Dec 2020, 22:16
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Bunuel wrote:
Define x?y to be |x - y| for all real numbers x and y. Which of the following statements is not true?


(A) x?y = y?x for all x and y

(B) 2(x?y) = (2x)?(2y) for all x and y

(C) x?0 = x for all x

(D) x?x = 0 for all x

(E) x?y > 0 if \(x \neq y\)



x?y = |x - y|

(A) x?y = y?x for all x and y

|x - y| = |y - x|
True for all x and y

(B) 2(x?y) = (2x)?(2y) for all x and y

2|x - y| = |2x - 2y|
True for all x and y

(C) x?0 = x for all x

|x - 0| = x
|x| = x
True if x >= 0 but false if x < 0 (in that case, |x| = -x)

(D) x?x = 0 for all x

|x - x| = 0
|0| = 0
True for all x

(E) x?y > 0 if \(x \neq y\)

|x - y| > 0
An absolute value is either 0 or positive.
|x - y| will be 0 only when x = y, else it will be positive.
True.

Answer (C)
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Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo [#permalink] New post   08 Dec 2020, 22:42
Given: Define x?y to be |x - y| for all real numbers x and y.
Asked: Which of the following statements is not true?


(A) x?y = y?x for all x and y
|x-y| = |y-x| : TRUE

(B) 2(x?y) = (2x)?(2y) for all x and y
2|x-y| = |2x-2y|; TRUE

(C) x?0 = x for all x
|x-0| = x; NOT NECESSARILY TRUE

(D) x?x = 0 for all x
|x-x|=0 ; TRUE

(E) x?y > 0 if \(x \neq y\)
|x-y|> 0 if \(x \neq y\); TRUE

IMO C
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Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo [#permalink]
08 Dec 2020, 22:42
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