SOLUTION: Let symbol ~ be defined so that a~b equals the smaller of a-b and b-a. For all real numbers a and b, all of the following are true EXCEPT: a) a~b = b~a b) a~b = (-a) ~ (-b) c)

Algebra.Com
Question 319194: Let symbol ~ be defined so that a~b equals the smaller of a-b and b-a. For all real numbers a and b, all of the following are true EXCEPT:
a) a~b = b~a
b) a~b = (-a) ~ (-b)
c) a~b < 0
d) a~0 = 0 ~ (-a)
e) If a>b>0, then (a~b)~b = -a
The answer key tells me that the correct answer is C, but it seems to me that using any combination of numbers will always result in a negative response.
Two negatives: -3 - (-5) = 2 *************** -5 - (-3) = -2
Two positives: 5-4=1 ************ 4-5= -1
One negative one positive: 5- (-3)= 8 **************** -3 - (5) = -8
Does 0 count as a real number? Is that why the solution is what it is?

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
It doesn't say that 'a' and 'b' have to be different numbers. If , then which means that and also. So this means that a ~ b < 0 is NOT true.
RELATED QUESTIONS

Let symbol ~ be defined so that a~b equals the smaller of a-b and b-a. For all real... (answered by jim_thompson5910)
Badbury is currently having a sale on their 1 kg bags of assorted chocolates (which... (answered by stanbon)
Let the operation § be defined for all positive integers a and b by the equation (answered by jim_thompson5910)
For all numbers x and y, let the operation * be defined by x * y = x - y. If a and b are... (answered by jim_thompson5910)
Let the operations ♦ and ♥ be defined for real numbers a and b a ♦... (answered by Fombitz,stanbon)
Let # be the binary operation defined on the positive real numbers by a#b=a^b. Find the... (answered by josgarithmetic)
Let a and b be real numbers. For this problem, assume that a - b = 4 and a^2 - b^2 = 8. (answered by MathLover1,greenestamps)
Let a and b be real numbers. For this problem, assume that a - b = 4 and a^2 - b^2 = 8. (answered by mccravyedwin,ikleyn)
for all numbers x and y, let the operation _ be defined by x _ y = xy - y. If a and b are (answered by Edwin McCravy)