Problem

My Observations 1) among all the people who have same choices at most one could be satisfied. so I removed all except one. 2) now I without proper reasoning I thought that some food groups will form and for each group its size — 1 will be added to answer. 3) I coded this approach using DSU and it worked I got an AC

but the problem is I am not able to justify the reasoning behind point number 2

My Solution Please tell me how my assumption is correct. Thanks and Regards