First off, there is no relation between number of tuples in the result of outer join and the number of ATTRIBUTES.
Assuming you meant to say that m and n denotes the number of tuples in R and S where R and S are the relations that are being full outer joined, then the minimum possible number of tuples are max(m,n) and the maximum possible number of tuples are (m+n).
Here if we perform (R outer full join S) then the result will be
This the maximum possible number of tuples that can be present in FULL JOIN, that is (m+n)
if I am mistaken please feel free to comment
it is M x N you can google it
The maximum number of tuple you will get is M x N. You have not considered the join condition in this case. Join operation involves cartesian product of both the tables first which will give you M x N tuples. Now if all the tuples satisfies this join condition then, the maximum number of tuples you will get is M x N.
the actual reason for this is – if you have two relation say R and S and suppose both share a common attribute A based on which they will be join then for join and we will get M x N tuples the worst case would be that if each tuple in m*n will satisfy the join condition.
an example of this would be suppose R.A has all value 1 in every tuple of R and S.A too have all value of A as 1
and join condition will be R.A = S.A then all the tuple will satisfy the condition