An anti-virus software would prevent your computer to be infected with many kinds of virus as long as its treat recognition databases match the potential treat's signature, but it can't possibly know all the different viruses that are out there, so stating that he is free from virus/trojan is plain wrong.
There's also another kind of malicious software, called malware, that most anti-viruses aren't aware of, and would let them pass through their protection without any alert. This so-called malware is just like any other regular software, but serves another purpose. That's why there is anti-malware software, these special kind of protection keeps a different kind of signature database that best fits malware's behaviours.
So the ideal thing would be to have both anti-virus and anti-malware protection, but the best is to always have common sense and avoid downloading stuff from non-trusted sites.