The objectives are

- Identify properties of relations
- Apply relational operators (excepting join)
- Prove properties of relational operators
- Represent binary-relations as graphs
- Represent binary-relations as matrixes

The book notation and the class notation is slightly different. Here is how the two are related given that $R$ and $S$ are relations:

- The select operation is identified by $\sigma_C\ R$ in class, but $s_C(R)$ in the book. In both cases $C$ is an expression that determines when a row is
*selected*and when it is not. - The project operation is identified by $\pi_{i_1i_2i_3\ldots}\ R$ in class but $P_{i_1i_2i_3\ldots}(R)$ in the book. In both cases, the columns in the subscript are the columns that remain.
- The natural join operation is identified by $R \bowtie S$ in class, but $J_p(R,S)$ in the book.
- The book does not define a rename operation identified by $\rho_{A \leftarrow B}\ R$ to indicate that $A$ becomes $B$ in the schema.

All problems are worth 3 points and reference problems in the course text.

- (4 points) 9.1.4 (int'l 7.1.4)
- (8 points) 9.1.6 (int'l 7.1.6)
- (2 points) 9.1.10 (int'l 7.1.8 also missing the word both before symmetric in part a)
- (1 points) 9.1.12 (int'l 7.1.10)
- (2 points) 9.1.38 (int'l 7.1.36; 8th ed. 9.1.40)
- (5 points) 9.1.50 (int'l 7.1.48; 8th ed. 9.1.52)
- (2 points) 9.2.26 (int'l 7.2.26)
- (2 points) 9.2.28 (int'l 7.2.28 change to Part_needs and Part_number) Express your answer to part a using $\pi$, $\sigma$, and $\rho$.
- (5 points) 9.3.14. Example 5 defines the $\circ$-operator. It relies on that $\odot$-operator that indicates Binary product. Binary product is defined in 2.6 example 8 (p. 182; 8th ed. p. 192) of the text. Intuitively $M_a \odot M_b$ is matrix multiplication only the multiply uses Boolean $\wedge$-operator to multiply two elements and the addition operator uses the Boolean $\vee$-operator to sum the multiplied elements. (int'l 7.3.14)
- (1 points) 9.3.28 (int'l 7.3.28) If you see a point that is unlabeled, it should be an “a”, matching the position of the four points on the other problems.
- (1 points) 9.4.28 part a only (int'l presumably 7.4.28; 8th edition needs to be checked, as well)