[Haskell] Translating Logical Statements

Translate the following statements into a logical statement using (forall, exists, and, or, imp, not). Then translate the statement into a Haskell variable which can be determined if true or not based on Q.

Given a set of numbers Q = {1, 2, 3, 4, 5, 6, 7, 8} ** will be used for all statements **

Example:

"Every number that's greater than 2 is greater than 1"

Logical Statement: forall n, (n > 2) imp (n > 1)

var = and [(n > 2) <= (n > 1) | n <- Q] ** each var should either return true or false when using Haskell interpreter **

1.) Every number is either greater than 1 or less than 2

Logical Statement:

var =

2.) Every two numbers are comparable with <= (i.e., either one is <=

-- the other or vice-versa)

Logical Statement:

var =

3.) There is an odd number greater than 4

Logical Statement:

var =

4.) There are two odd numbers that add up to 10

Logical Statement:

var =

5.) For every even number, there is a greater odd number

Logical Statement:

var =

6.)There are two odd numbers that add up to 6

Logical Statement:

var =