For typing convenience, I'll use $R,S$ for $R_1,R_2$ respectively. Similarly, $m,n$ instead of $N_1,N_2$

Given $n > m>0.$

**Schema assumption** for expressions $R \cup S, R \cap S, R -S :$ They must be Union Compatible i.e. For these Set Operations to be valid, we require that two conditions hold:

1. The relations $R$ and $S$ must be of the same arity. That is, they must have the same number of attributes.

2. The domains of the $i-th$ attribute of $R$ and the $i-th$ attribute of $S$ must be the same, for all $i.$

Note that $R$ and $S$ can be either database relations or temporary relations that are the result of relational-algebra expressions.

1. $R \cup S :$ Max = $m+n $ (When R,S are disjoint sets) ; Min = $max(m,n) $ which is $n$ here (Min when one relation is subset of other )

2. $R \cap S :$ Max = $min(m,n) = m $ (when one relation is subset of other) ; Min = $0 $ (When R,S are Disjoint sets )

3. $R -S : $ Max = $m $ (When R,S are disjoint sets) ; Min = $0 $ (When R is subset of S )

4. $R \times S :$ No schema assumptions required.

Max, Min = $m.n$

5. $\sigma_{a =5}R :$

Schema Assumption : In the schema of $R,$ there should be an attribute by the name $'a'.$ Moreover, the domain of this attribute $'a'$ must contain $5.$

Max = $m$ (When all the tuples of $R$ have value of attribute $a$ as 5.)

Min = 0 (When None of the tuples of $R$ have value of attribute $a$ as 5.)

6. $\prod_aR : $

Schema Assumption : In the schema of $R,$ there should be an attribute by the name $'a'.

Max = $m$ (When None of the two tuples of $R$ have same value of attribute $a.$)

Min = **1 **(When all the tuples have same value for attribute $a.$)

7. $R/S :$

Schema Assumption : Let relation R,S have X,Y set of attributes respectively. Then $R/S$ to be valid, We have $X \supset Y.$ (Y must be proper subset of X.)

For the given Question :

Max, Min = 0 (Because $n > m$)

In General, For $R/S :$

If $m \geq n, $ and $n \neq 0,$ then Max = Floor$(m/n),$ Min = 0

If $n = 0$ then Max = $m$ (When $X-Y$ have distinct values in all tuples), Min = 1 if $m \neq 0$ and All the tuples have same value for $X-Y$, Or Min = 0 if $m=0$