1. TRUE or FALSE: Ayer defends the traditional "justified true belief" analysis of knowledge; on his formulation of it, if a claim is true, you're sure it's true, and you have the "right" to be sure it's true, you know it—and you only know it if all three of these conditions hold.
2. TRUE or FALSE: According to Ayer, you can only know the truth of a mathematical statement (such as that the angles of a triangle add up to 180°) if you can give a full proof of it; being able to give the correct answer, based on having learned it in the past from an authoritative source, isn't enough.
3. TRUE or FALSE: According to Ayer, you only have the right to be sure of something if you know exactly how you know it; e.g., he says that someone who could confidently and reliably predict lottery numbers with 100%accuracy, based on a feeling or "intuition," couldn't be said to really know what those numbers will be.
4. TRUE or FALSE: In Gettier's example, Smith believes a truth ("The man who will get the job has 10 coins in his pocket") based on the fact that it follows logically from something he has good reason to believe, but is false.
5. TRUE or FALSE: The point of Gettier's example is to show that having the right to be sure is not necessary for knowledge, and that any true belief counts as knowledge.
8. TRUE or FALSE: If we let p = you are not a brain in a vat, then substituting this into Nozick's third condition (3) results in "If you were a brain in a vat, you wouldn't believe you were not"; Nozick's analysis implies that this statement must be true for you to know that you're not a brain in a vat.
It's been a long time since I read any Ayer though, so check these against your own discriminative faculties.