Entity Framework 4.0: Error 113: Multiplicity is not valid in Role
Right click on the relationship in your EDX diagrame. In proprety, change END1 Multiplicity to 0..1 (Zero or One of YOURTABLENAME)
If your FK is nullable your multiplicity in principal entity must be 0..1 - default value has no role in this because you can assign null to FK. So all your dependent entities must be in 0..1 - * relation with your principal entity.
I just had the same message and it was perplexing because the tables I modified in the DB were different from the ones I was getting the message for.
I tried changing the multiplicity 0..1-to-many but the message persisted, even after "Run Custom Tool" commands, cleans and rebuilds.
Resolved by dropping the relationship EF was complaining about and updating the model from DB
I deleted the updated table from the model and then in Update Model from Database, added it again and it helped.