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SOP is necessary because that indicates your study plan, people provide justification in the same letter or provide an additional Letter of explanation regarding the specific refusal reasons alongwith a study plan!
 
You don’t have to name these letters. We can call them anything at all! Just make sure you mention your study plan (hence the SOP) and you should obviously tackle all rejection points (the justification letter).

you can write a combined letter or be more organized and make 2 with proper approach. All the best!
 
SOP AND JUSTIFICATION LETTER IS REQUIRED FOR VISA REAPPLICATION OR ONLY JUSTIFICATION IS SUFFICE.
Write a SOP which address the concerns expressed in your refusal letter in detail. You don't have to name this letter with any specific titles other than just Statement of Purpose.
Good luck