OK, there are a couple of problems here:
1) SDF is not VB specific: if's a database format which can be used by any .NET application, provided it has the SQLCE assemblies referenced. MDF files are Access databases and need different classes in your code, and well as a suitable ACE or JET driver installed - unless you are using SQL Server and attaching the DB that way. Even then, you will need SQLConnection, SQLCommand and suchlike objects to access it.
2) You can't just write a connection string like that!
DBMSConnectionString="DataSource(LocalDB)\v11.0;AttachDbFilename="C:\\Users\\user-name\\documents\\visual studio 2013\\Projects\\library mangement system\\library mangement system\\LMS.mdf";Integrated Security=True");
I'm not possitive I know what you re trying to do there, but this
might work a little better:
DBMSConnectionString="DataSource(LocalDB)\v11.0;AttachDbFilename=\"C:\\Users\\user-name\\documents\\visual studio 2013\\Projects\\library mangement system\\library mangement system\\LMS.mdf\";Integrated Security=True");
But I'd start by creating a connection in VS and base it on the connections string from there:
1) Open the Server Explorer pane.
2) Right click "Data connections" and select "Add connection"
3) In the dialog that follows, select your DataSource, and database, specify the security info, and press the "Test connection" button.
4) When the connection works, press "OK"
5) Highlight your database in the Server Explorer pane, and look at the Properties pane. A working example of the connection string will be shown, which you can copy and paste into your app or config file.
Since you are attaching the file each time (why?) you may have to tweak this.