In the twelve labors of hercules what labor is the hardest

  this riddles' answer is library.

  the "leaves" are a reference to the books' pages that the library contains; the branches are a network of libraries that connect multiple libraries' collections, resources, and items in a system of a common database, integrating them; the branches' organization are a useful management tool for coordinating the multiple collections many libraries have.

your answers are correct.

the correct definition of purity is like something being pure.

ex. the girl was so pure(ity) she was so sweet and gentle, that she couldn't even hurt a fly.

ex. the man had so mch purity he didn't even know how to curse.