In practical analysis, to believe and know requires 2 reconditions: Necessary and sufficient, to give a good account of what you are analyzing.
1) Can a person know that p is true if they believe that p is true?
2) Can a person know that p is true if they do not believe p is true?
3) Can a person think they know p if in fact, p is false?
4) Can a person reasonably think they know p if p is false?
5) Can a person know p if in fact p is false?
This brings us to a huge Epistemological problematic issue.
Imagine being the victim of a prank like this:
Imagine you wake up on a table after a big roaring drunk party, and see your friend on the next table. Surgeons are apparently removing his brain and hooking it up to a wire harness and suspending it in a nutrient tank. You have reliable evidence that you're next, so you protest that you don't want that, and that you aren't going to do it. The surgeon chuckles, and tells you relax, it had been done to you 3 months ago, and the entire 3 months previous were a computer generated illusion.
Is he lying to you? Do you know that that reality you've been experiencing is true or are you actually a brain in a tank?
Next, they tell you it was all a prank. Are they lying to you now, or were they before, and how would you determine the truth of either statement? What is belief, and what is knowledge?