Core is a synonym of Memory. Memory is related to Mental. Mental is a synonym of Chin. 
General is related to Command. Command is the opposite of Serve. Admit is a type of Serve. Apologize entails/necessarily involves Admit. 
Core <--Synonym--> Memory <--RelatedTo--> Mental <--Synonym--> Chin 
General <--RelatedTo--> Command <--Antonym--> Serve <--IsA-- Admit <--Entails-- Apologize 