Surely there are women in the world who are not brilliant. On the other hand, the major premise of the second syllogism we can accept as true. While there may in fact be people who have been exposed to this virus and lived, we have no record of them. On the other hand, every case of E-Boli that we've seen has resulted in death. Therefore, we can proceed confidently from our major premise to a conclusion that is sound.
Abortion is murder.
Abortion is a terrible crime. In this case, it is the minor premise that is most open to challenge. If the writer can convince his reader that it is, then the reader will accept his conclusion. This way of arguing is called deduction. When one deduces, she moves from a general argument to a specific argument.