I haven't used the relations package before, but it looks like this works:
import Data.Relation
symmetric :: Ord a => Relation a a -> Bool
symmetric rel = and [member b a rel | (a, b) <- toList rel]
To test:
> symmetric $ fromList [(1, 2), (2, 1)]
True
> symmetric $ fromList [(1, 2), (2, 3)]
False