<P> Gettier's case is based on two counterexamples to the JTB analysis . Each relies on two claims . Firstly, that justification is preserved by entailment, and secondly that this applies coherently to Smith's putative "belief". That is, that if Smith is justified in believing P, and Smith realizes that the truth of P entails the truth of Q, then Smith would also be justified in believing Q. Gettier calls these counterexamples "Case I" and "Case II": </P> <Dl> <Dd> Suppose that Smith and Jones have applied for a certain job . And suppose that Smith has strong evidence for the following conjunctive proposition: (d) Jones is the man who will get the job, and Jones has ten coins in his pocket . </Dd> </Dl> <Dd> Suppose that Smith and Jones have applied for a certain job . And suppose that Smith has strong evidence for the following conjunctive proposition: (d) Jones is the man who will get the job, and Jones has ten coins in his pocket . </Dd> <Dl> <Dd> Smith's evidence for (d) might be that the president of the company assured him that Jones would, in the end, be selected and that he, Smith, had counted the coins in Jones's pocket ten minutes ago . Proposition (d) entails: (e) The man who will get the job has ten coins in his pocket . </Dd> </Dl>

The gettier problem challenges which of the following conceptions of knowledge