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- | This homework covers sections 5.1 and 5.3 | ||

- | ==Objectives== | + | The objectives are |

- | * Practice inductive proofs applied to different problem domains | + | * Identify properties of relations |

- | * Identify faulty reasoning in inductive proofs | + | * Apply relational operators (excepting join) |

+ | * Prove properties of relational operators | ||

+ | * Represent binary-relations as graphs | ||

+ | * Represent binary-relations as matrixes | ||

- | ==Problems for all sections== | + | ==Problems== |

- | All problems are worth 3 points. | + | 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. | ||

- | # 5.1.4 | + | All problems are worth 3 points and reference problems in the course text. |

- | # 5.1.6 | + | |

- | # 5.1.10 | + | # (4 points) 9.1.4 (int'l 7.1.4) |

- | # 5.1.18 | + | # (8 points) 9.1.6 (int'l 7.1.6) |

- | # 5.1.26 | + | # (2 points) 9.1.10 (int'l 7.1.8 also missing the word both before symmetric in part a) |

- | # 5.1.38 | + | # (1 points) 9.1.12 (int'l 7.1.10) |

- | # 5.1.42 | + | # (2 points) 9.1.38 (int'l 7.1.36; 8th ed. 9.1.40) |

- | # 5.1.50 | + | # (5 points) 9.1.50 (int'l 7.1.48; 8th ed. 9.1.52) |

- | # 5.4.18 '''(Sections 1 and 2 -- don't do this problem)''' | + | # (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) |