Approve is etymologically related to Improve. 
Vitamin is a type of Medicine. Medicine is related to Heal. Heal is the opposite of Harm. Harm is related to Dangerous. 
Approve --EtymologicallyRelatedTo--> Improve 
Vitamin --IsA--> Medicine <--RelatedTo--> Heal <--Antonym--> Harm <--RelatedTo--> Dangerous 