Do not understand this problem... Can someone help explain with an answer? If so, it would be a great help. Will vote best answer.
-
For all of these cases, we will consider three distinct real numbers a, b, and c.
For all of these cases, I will assume strict inequalities (just greater than and less than).
the reflexive property means that a > a. This is never true, so the reflexive property does not hold.
the symmetric property states that if a > b then b > a. This is never true, so the symmetric property does not hold.
the transitive property states that if a > b and b > c, then a > c. This property holds for inequalities.
If non-strict inequalities are considered (including greater than or equal to and less than or equal to) then the reflexive property would hold (a >= a always), but the symmetric property would not hold (since I stated a, b, and c were distinct).
For all of these cases, I will assume strict inequalities (just greater than and less than).
the reflexive property means that a > a. This is never true, so the reflexive property does not hold.
the symmetric property states that if a > b then b > a. This is never true, so the symmetric property does not hold.
the transitive property states that if a > b and b > c, then a > c. This property holds for inequalities.
If non-strict inequalities are considered (including greater than or equal to and less than or equal to) then the reflexive property would hold (a >= a always), but the symmetric property would not hold (since I stated a, b, and c were distinct).