Compete requires Improve. Improved is a form of Improve. 
Juice is related to Milk. Milk is related to Infant. Infant is related to Egg. Egg is related to Cholesterol. 
Compete --HasPrerequisite--> Improve <--FormOf-- Improved 
Juice <--RelatedTo--> Milk <--RelatedTo--> Infant <--RelatedTo--> Egg <--RelatedTo--> Cholesterol 