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

Question

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 
eq y

Archit3110 · Answer

for x?0 = x for all x
0>x
not sufficient
IMO C

stne · Answer

Yes if X = -2 then x?y
|-2-0|=2 which is  
eq  -2
Hence C is not true .

Deepakjhamb · Answer

Substitute numbers in the range and we can setup this

Posted from my mobile device

Deepakjhamb · Answer

Substitute numbers in the range and we can setup this

Posted from my mobile device

KarishmaB · Answer

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 
eq 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)

Kinshook · Answer

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 
eq y 
|x-y|> 0 if  x 
eq y ; TRUE

IMO C

bumpbot · Answer

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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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