Apologize entails/necessarily involves Admit. Admit is a type of Serve. Serve is the opposite of Command. Command is related to General. 
Comedy is the opposite of Horror. Horror is a type of Thing. Thing is related to Flower. Flower is the opposite of Leaf. 
Apologize --Entails--> Admit --IsA--> Serve <--Antonym--> Command <--RelatedTo--> General 
Comedy <--Antonym--> Horror --IsA--> Thing <--RelatedTo--> Flower <--Antonym--> Leaf 