I'm new to SF and validation rules. Wondering if anyone might have insight into rewriting this validation rule and can help explain the logic to me?

So this is the current validation rule set up that throws the error: 

/*this is a comprehensive list of all text values we want to allow in the "Division" field*/ 

if(Division="Lightcast",false, 

/*Public Sector divisions*/ 

if(Division="Public Sector",false, 

if(Division="EDO",false, 

if(Division="National Public Sector",false, 

if(Division="State and Local Public Sector",false, 

if(Division="Workforce",false, 

/*Education divisions*/ 

if(Division="Education",false, 

if(Division="Colleges",false, 

if(Division="EDU Partnerships",false, 

if(Division="University",false, 

/*Global divisions*/ 

if(Division="Global",false, 

/*Enterprise divisions*/ 

if(Division="Enterprise",false, 

if(Division="Enterprise Carlone",false, 

if(Division="Enterprise Semmes",false, 

if(Division="Enterprise Global",false, 

if(Division="Enterprise Mid Market",false,true)))))))))))))))) 

I'm attempting to re-write it to make it somewhat more complex, but perhaps less clunky. We want the Division field on users to sort of function as if it were a dependent picklist related to the Lightcast Market Vertical field. If we choose "Public Sector" for a user in that Lightcast Market Vertical field, then we want the ONLY acceptable text options in the Division field to be one of the 5 Public Sector text options. Similarly, if we choose "Education" in the Lightcast Market Vertical field, then we want the validation rule to only allow text to be one of those 4 relevant Education text options. Etc. Hope that makes sense. Any suggestions?