A sentence is a proposition if it has a truth value; in other words, it is a statement (not a question, not a command, ...) that is either true or false.
Originally Posted by bugbear
The difference of two primesis not a proposition, because it isn't a statement. In fact, it isn't even a sentence.
Examples of propositions are:
All cows have six legs.(The first is clearly false, the second is true. For the third, it's only a proposition provided the term 'good-looking' has been unambiguously defined.)
The Pacific Ocean is the deepest ocean in the world.
Every mathematics lecturer is good-looking.
But examples of sentences that aren't propositions include:
Eat more chocolate!(Note that, although the second of these can be answered by 'Yes', it doesn't make it a proposition: it's a question.)
Is 6 greater than 2?
Why is logic so hard?
To write the negation of a proposition, you can always write in front of it the phrase:
It is not true that ...Try it with the three propositions above. You'll see that each one now has the opposite truth value.
(By the way, have you now solved your original questions 2 and 3?)