## Writing formal propositions

First write the following propositions using quantifiers. Then negate them, and finally write the negated propositions informally, like the original propositions.

• #### Variant 1

All natural numbers are even.

• #### Variant 2

Every prime number is odd.

• #### Variant 3

Some natural number is divisible by all primes.

• #### Variant 4

Between $$n$$ and $$2n$$ we can always find some prime number.