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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

## Problems

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.

1. (4 points) 9.1.4 (int'l 7.1.4)
2. (8 points) 9.1.6 (int'l 7.1.6)
3. (2 points) 9.1.10 (int'l 7.1.8 also missing the word both before symmetric in part a)
4. (1 point) 9.1.12 (int'l 7.1.10)
5. (2 points) 9.1.38 (int'l 7.1.36)
6. (5 points) 9.1.50 (int'l 7.1.48)
7. (2 points) 9.2.26 (int'l 7.2.26)
8. (2 points) 9.2.28 (int'l 7.2.28 change to Part_needs and Part_number)
9. (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 on page 182 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)
10. (1 points) 9.3.28 (int'l 7.3.28)
11. (1 points) 9.4.26 part a only (int'l 7.4.26)