Hello bugbear Originally Posted by

**bugbear** one more question, how to determine whether the sentence is proposition? and if its a proposition, how to write its negation?

for example this sentence,

Code:

The difference of two primes.

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*.

So obviously

The difference of two primes

is 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 Pacific Ocean is the deepest ocean in the world.

Every mathematics lecturer is good-looking.

(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.)

But examples of sentences that aren't propositions include:

Eat more chocolate!

Is 6 greater than 2?

Why is logic so hard?

(Note that, although the second of these can be answered by 'Yes', it doesn't make it a proposition: it's a question.)

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?)

Grandad