After conducting a thorough analysis of the relationship between the feature "purpose" and the task of determining whether a person receives credit or not, I have identified the following details:

- Possible values of feature "purpose" for the target class "yes" (person receives credit): ['radio/tv', 'education', 'furniture/equipment', 'new car', 'used car', 'business', 'domestic appliance', 'repairs', 'retraining']
- Possible values of feature "purpose" for the target class "no" (person does not receive credit): ['other']

Based on this analysis, the dictionary representation of the relationship between the feature and target is as follows:

```json
{
	"yes": ["radio/tv", "education", "furniture/equipment", "new car", "used car", "business", "domestic appliance", "repairs", "retraining"],
	"no": ["other"]
}
```