Hi guys,

I'm struggling to take on these questions where I am asked to write propositions using connectives and quantifiers:

Let P(x) be the statement that says that a real number x has some property P.

For every two real numbers x and y with x<y, there is a real number with the property P between x and y.

I must also construct a negation for this problem. There is also a very similar question to this that I have to do but instead of using P(x) as the statement that says a real number x has some property P, I must let P(n) be the statement that says that a natural number n has some property P then write the following statement using connectives and quantifiers:

Any sum m + n of natural numbers m and n which have the property P, has the property P.