Consider a relational table $r$ with sufficient number of records, having attributes $A_1, A_2, \dots, A_n$ and let $1 \le p \le n$. Two queries Q1 and Q2 are given below. Q1: $\pi_{A_1, \dots, A_p}(\sigma_{A_p = c}(r))$ where $c$ is a constant Q2: $\pi_{A_1, \dots, A_p}(\sigma_{c_1 \le A_p \le c_2}(r))$ where $c_1$ and $c_2$ are constants The database can be configured to do ordered indexing on $A_p$ or hashing on $A_p$. Which of the following statements is TRUE?

• Q1 is an equality/point query (exact match $\sigma_{A_p = c}$). Hashing provides direct access with average time complexity $O(1)$, which is generally faster than ordered indexing (e.g., $\text{B}^+$ tree) which has $O(\log N)$ lookup time. Thus, hashing outperforms ordered indexing for Q1.

• Q2 is a range query ($\sigma_{c_1 \le A_p \le c_2}$). Ordered indexing stores keys in sorted order, which allows finding the starting key and traversing sequential leaf nodes efficiently. Standard hashing does not preserve order, so a range query would require scanning all buckets/records. Thus, ordered indexing outperforms hashing for Q2.

Therefore, hashing will outperform ordered indexing on Q1, but not on Q2.

Hence, the correct option is (C).