Problem 109 (difficulty: 4/10)

Using the field and ordering axioms prove the following statements:

 (1)  If \(\displaystyle a<b\), then \(\displaystyle -a>-b\);
 (2)  If \(\displaystyle a>0\), then \(\displaystyle \frac{1}{a}>0\);
 (3)  If \(\displaystyle a<b\) and \(\displaystyle c<0\), then \(\displaystyle ac>bc\).

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