Final answer:
Kwashiorkor is the deficiency state associated with a symmetric rash around the neck due to protein deficiency.
Step-by-step explanation:
A symmetric rash around the neck is a characteristic symptom of kwashiorkor, which is a severe form of protein deficiency. Kwashiorkor occurs when a child's diet lacks sufficient protein, leading to various symptoms including skin problems and weak muscles.
The rash is often accompanied by other signs such as swollen bellies and feet.
It is important to address this deficiency and provide the necessary nutrients for proper growth and development.