cross-purpose vs incongruity

cross-purpose

noun
  • A contrary or conflicting purpose or understanding, especially an unintentional or misconceived one. 

incongruity

noun
  • An instance or point of disagreement 

  • A thing that is incongruous. 

  • The state of being incongruous, or lacking congruence. 

How often have the words cross-purpose and incongruity occurred in a corpus of books? (source: Google Ngram Viewer )