could anyone please help me solving these problems?
thanks a lot!
A) prove that if a,b,c is in the ordered integral domain D and its given that a<0 and b<0 then prove that ab>0... have no idea how to approach!
B) prove that if a,b is in the ordered integral domain (D^p) and its given that a>b then prove that a^2>b^2...
--------> I know a little bit of the solution for this particular problem but not sure if this is the correct way to approach it.
we know from the ordered integral domain theorem part (c) that "Exactly one of the following is true: a=b, a>b or b>a"
a > b and a > 0 imply a^2 > ab, and a > b and b > 0 imply ab > b^2.
so by the same theorem part (g), a^2 > ab > b^2 implies a^2 > b^2.
thanks for the help!