Post form array data to php for comparison and get output

I want to create a form which will have array stored into it. This array should be sent to php for comparison with another array without html page refresh, keeping already selected options and after comparison, user should be notified match. I have created php to compare. I also have created form in html which saves array. I attempted to make use of ajax to send information, but somehow not working. I am quite sure that I am making some silly mistake, though, I still don't know how to dynamically pop up the match information after comparison is done. Hence, I want somebody to help me. I will provide what I have done so far and freelancer needs to complete remainder to achieve my objective.