belief vs dilemma

belief

noun
  • Mental acceptance of a claim as true. 

  • Religious faith. 

  • One's religious or moral convictions. 

  • The quality or state of believing. 

  • Faith or trust in the reality of something; often based upon one's own reasoning, trust in a claim, desire of actuality, and/or evidence considered. 

  • Something believed. 

dilemma

noun
  • A type of syllogism of the form "if A is true then B is true; if C is true then D is true; either A or C is true; therefore either B or D is true". 

  • A difficult circumstance or problem. 

  • A circumstance in which a choice must be made between two or more alternatives that seem equally undesirable. 

  • Offering to an opponent a choice between two (equally unfavorable) alternatives. 

How often have the words belief and dilemma occurred in a corpus of books? (source: Google Ngram Viewer )