and :: [Bool] -> Bool
-- testing 14 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 3 candidates of size 2
-- looking through 6 candidates of size 3
-- looking through 6 candidates of size 4
-- looking through 16 candidates of size 5
-- looking through 41 candidates of size 6
-- looking through 103 candidates of size 7
-- looking through 278 candidates of size 8
-- looking through 752 candidates of size 9
and ps  =  null ps || head ps && and (tail ps)

or :: [Bool] -> Bool
-- testing 14 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 3 candidates of size 2
-- looking through 6 candidates of size 3
-- looking through 6 candidates of size 4
-- looking through 16 candidates of size 5
-- looking through 41 candidates of size 6
-- looking through 103 candidates of size 7
-- looking through 278 candidates of size 8
-- looking through 752 candidates of size 9
-- looking through 1963 candidates of size 10
-- looking through 5427 candidates of size 11
or ps  =  not (null ps || not (head ps || or (tail ps)))

and :: [Bool] -> Bool
-- testing 14 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 3 candidates of size 2
-- looking through 6 candidates of size 3
-- looking through 8 candidates of size 4
and ps  =  foldr (&&) True ps

or :: [Bool] -> Bool
-- testing 14 combinations of argument values
-- looking through 2 candidates of size 1
-- looking through 3 candidates of size 2
-- looking through 6 candidates of size 3
-- looking through 8 candidates of size 4
or ps  =  foldr (||) False ps