Five Properties: basic proofs
I'm not expecting anyone to answer all of these, but hopefully someone can do one for me. It seems pretty straightforward and I wouldn't be posting if I had time to talk to my prof. before my exam tomorrow. Again, only using the 5 rules .
(1) For any real numbers a and b and any positive real number c.
a < b => ac < bc
(2) For any real number a,
a is positive <=> -a is negative
(3) For any real numbers a, b, c
if a < b and c is negative, then ac > bc
(4) For any real numbers a and b
ab is positive <=> a and b are both positive or both negative
(5) -1 < 0 < 1
USING ONLY THESE RULES
(a) a^2>=0 for any a
(b) For any real number a, if a is positive, then 1/a is positive.
(c) For any positive real numbers a and b, if a < b, then 1/a > 1/b