Aproblem exists when the current condition differs from a desired condtion. this idea defines which step in problem solving

A problem exists when the current condition differs from a desired condition. This idea defines the first step in problem solving.

Explanation:

Problem solving has many steps to solve the problem which may range from 4 to 8 steps. In this step by step process the first step is to identify the problem. A problem will only exist when the desired effect is different from the effect it is currently producing.  

The next step is to find a solution. Once a solution is formulated then the ways and means of solving it has to be studied. The pros and cons of the solution have to be carefully analysed. Then only can the problem be effectively solved and the process of problem solving be completed.  

do you have more to the question?

the sentence does not violate the phrase structure second rule (introduced by noam chomsky) because noun phrases consist of a determiner such as a, the or every, and a noun. in the sentence, the noun phrase the cake includes a determiner (the) and a noun (cake).

on the other hand, the first rule indicates that a sentence encloses a noun phrase, followed by a verb phrase. the example sentence can be analysed as follows:

john (n) + ate (v) + the (det) + cake (n).