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cs-236:homework-7 [2015/01/05 13:40]
egm [Problems for all sections]
cs-236:homework-7 [2018/11/30 17:25]
pdiddy [Problems]
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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.
  
-# (points) ​5.1.4 +All problems are worth 3 points and reference problems in the course text. 
-# (points) ​5.1.6 + 
-# (points) ​5.1.10 +# (points) ​9.1.4 (int'l 7.1.4) 
-# (points) ​5.1.18 +# (points) ​9.1.6  ​(int'​l 7.1.6) 
-# (points) ​5.1.26 +# (points) ​9.1.10 (int'l 7.1.8 also missing the word both before symmetric in part a) 
-# (points) ​5.1.38 +# (points) ​9.1.12 (int'l 7.1.10) 
-# (points) ​5.1.42 +# (points) ​9.1.38  (int'l 7.1.36; 8th ed. 9.1.40) 
-# (points) 5.1.50 +# (points) ​9.1.50 (int'l 7.1.48; 8th ed. 9.1.52) 
-# (points) ​5.4.18 +# (points) ​9.2.26 (int'l 7.2.26) 
 +# (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 $\rho$. 
 +# (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) 
 +# (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
 +# (points) ​9.4.28 part a only (int'l presumably 7.4.28; 8th edition needs to be checked, as well)
cs-236/homework-7.txt · Last modified: 2018/11/30 17:25 by pdiddy
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