Consider this Scenario :

R (A,B) : 10000 rows ( showing Seperate Values Of A and B for a tuple/row)

A Tuples ( a1,a2,.......,a1001, (a1001,........ a1001) 8999 times ) B Tuples ( b1,b2,b3,.........,b10000 )

S (A,C) : 5000 rows ( showing Seperate Values Of A and C for a tuple/row)

A Tuples ( a1,a2,.......,a1001, (a1001,........ a1001) 3999 times ) C Tuples ( c1,c2,c3,.........,c5000 )

Now Making Join Of Both (Natural Join) ( For each tuple of R matching with Each tuple of S on basis of Common Column A)

For a1 : Match Found : 1 ; a2 : Match Found 1 ; ................ ; a1000 : Match Found 1 ; (Inidividual Match **(A)** :1000 )

For a1001 :

Match Found : For R -> A ( row no 1001) : With S -> A (row no 1001)

For R -> A ( row no 1001) : With S -> A (row no 1002)

... So 4000 matches for R -> A ( row no 1001 ) .... Similarly 4000 matches for R -> ( row no 1002) ....

For Others : 8999 a1001's of relation R -> Matches by Duplicate **(B)** : 9000 * 4000 = 36 * 10^6

Total Matches : **(A) + (B)** : 36000000 + 1000 = 36001000. (Answer)

P.S. : Here we are taking as many as duplicates in Relation R and S ; because we need to find maximum number of tuples.