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

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New post 19 Mar 2019, 02:07
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A
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C
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E

Difficulty:

  75% (hard)

Question Stats:

37% (01:36) correct 63% (01:42) wrong based on 56 sessions

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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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Re: Define x?y to be |x - y| for all real numbers x and y. Which of the fo  [#permalink]

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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]

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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] 19 Mar 2019, 11:56
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