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Tutors Answer Your Questions about real-numbers (FREE)
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?
Click here to see answer by jim_thompson5910(28555) |
Question 327328: Please help me solve this question:
Determine whether each statement is true or false and give a counterexample if the statement is false.
A. The set of rational numbers is closed under subtraction.
-10/(-2) = +5 = 5
B. The set of irrational numbers is closed under division.
Click here to see answer by Fombitz(13828)  |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790
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