A binary search tree is used to locate the number 43. Which of the following probe sequences are not possible?

A library relational database system uses the following schema

USERS (User #, User Name, Home Town)

BOOKS (Books # Book Title, Author Name)

ISSUED (Book #, User #, Date)

Explain in one English sentence, what each of the following relational algebra queries is designed to determine.

(a) $$\sigma_{ \text{User#}=6}\left(\pi_{\text{User#, Book Title}}\left(\left(\text{USERS} \bowtie \text{ISSUED}\right) \bowtie \text{BOOKS}\right)\right)$$

(b) $$\pi_{\text{Author Name}}\left(\text{BOOKS} \bowtie \sigma_{\text{Home Town=Delhi}} \left(\text{USERS} \bowtie \text{ISSUED}\right)\right)$$

A logic network has two data inputs $$A$$ and $$B,$$ and two control inputs $${C_0}$$ and $${C_1}$$. It implements the function $$F$$ according to the following Table.

Implement the circuit using one $$4$$ to $$1$$ Multiplexor, one $$2$$-input Exclusive $$OR$$ gate, one $$2$$-input $$AND$$ gate, one $$2$$-input $$OR$$ gate and one Inverter.

What is the equivalent Boolean expression in product-of-sums form for the Karnaugh map given in fig?