be up to vs let

be up to

verb
  • To do or be involved in doing; to do (often something mischievous or inappropriate). 

  • To depend on, to be the choice of. 

let

verb
  • To allow to be or do without interference; to not disturb or meddle with; to leave (someone or something) alone. 

  • To give, grant, or assign, as a work, privilege, or contract; often with out. 

  • Used to introduce a first or third person imperative verb construction. 

  • To cause (+ bare infinitive). 

  • To allow the release of (a fluid). 

  • To allow possession of (a property etc.) in exchange for rent. 

  • To allow to, not to prevent (+ infinitive, but usually without to). 

noun
  • The hindrance caused by the net during serve, only if the ball falls legally. 

  • An obstacle or hindrance. 

  • The allowing of possession of a property etc. in exchange for rent. 

How often have the words be up to and let occurred in a corpus of books? (source: Google Ngram Viewer )