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 ->  Expressions-with-variables -> 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)      Log On


   

Question 319222: 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) About Me  (Show Source):
You can put this solution on YOUR website!
The statement a~b < 0 means that a ~ b is less than zero for ALL values of 'a' and 'b'. However, if a=b, then a-b=a-a=0 and b-a=a-a=0 which basically means that a-b=b-a=0. So if a=b, then a ~ b = 0 meaning that a ~ b < 0 is NOT true. Does that make sense?