In Natural Join first we do the cross product then we do the selection and the selection is done in between the common attribute of the relation and when we don't have the common attribute then we simply do the cross product.
Case 1: In this, we have C as the common attribute so first we do the cross product and check where (R.C=S.C) then we select those tuples. so, in the result, we get (1,2,3,4)and(7,8,9,10) as 3 and 9 are common in C.
Case 2: In this, we have C as the common attribute we do the same procedure as above but here we don't have any common values in C. so in the result we will get the Empty relation as no tuple will be selected.
Case 3: In this we don't have any common attribute so we do the cross product only.