brush off vs look down one's nose

brush off

verb
  • To disregard (something), to dismiss or ignore (someone), as unimportant. 

  • Used other than figuratively or idiomatically: see brush, off. To remove something with a brush. 

look down one's nose

verb
  • To regard as inferior or distasteful; to hold in contempt. 

How often have the words brush off and look down one's nose occurred in a corpus of books? (source: Google Ngram Viewer )