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- 1. A known relationship mode of R (U, F), U= (c, t, h, r, s, g, q); F={c->tq, cs->g, ht->r,hr->c, hs->r}; find the minimum cover of F, then use the Normal Form decompositionalgorithm to standardize this mode to 3NF, and check if the decomposition has thenonadditive join property.Consider an equivalence relation R on X={a,b,c}. R= {(a,a), (a,c), (b,b), (c,a), (c,c) } [a]=Given the following UML diagram: Student - studentID: String + getStudentID(): String + toString(): String Person - lastName: String - firstName: String - dateOfBirth: Date - address: Address + getName(): String + getDOB(): Date + getAddress(): Address + toString(): String Professor - employeeID: String + getEmployeID(): String + toString(): String Write an implementation for the class Professor. DO NOT include or implement any constructor for this class. There are no abstract methods/classes in this example. toString method will return any simple String that contains firstName and employeelD only; no less, no more!! Assume firstName was defined as protected in class Person. You are not allowed to add implementation for any class or methods other than what is listed in the question statement. 2
- Question 4 Consider the relation R defined on the set Z x Z: R = {((a,b),(c,d)) | a = c (mod 4) a b = d (mod 7)}. Find the equivalence class of (3, 6) with respect to R. Note that Z represents the set of integers. O {a |a = b (mod 4) a a = b (mod 7)} O {a | a = b (mod 4) v a = b (mod 7)} {(a,b) | a = 3 (mod 4) a b = 6 (mod 7)} O {(c,d) | C = d (mod 4) v c = d (mod 7)} O {(a,b) | a = b (mod 4) v a =b (mod 7)} O {a|a = 3 (mod 4) a a = 6 (mod 7)} O {a | a = 3 (mod 4) v a = b (mod 7)} O None of the choicesLet A = {a, b, c, d} and R = {(a, a), (b, b), (c, c), (d, d), (a, d), (d, a), (b, c), (c, b)} an equivalence relation on A. Select the following sets that are equivalence classes of R {a, b} {a} {a,b,c} O{c, b} O{a, d} {a,b,c,d} {d} {c, d}PLEASE TYPE ONLY**** ANSWER ALL THREE QUESTIONS Exercise 8.1.4: Arrow diagrams for relations on small finite sets. Draw the arrow diagram for each relation. (b) The domain of relation P is {2, 4, 8, 16, 32, 64}. For x, y in the domain, xPy if there is a positive integer n such that xn = y. (c) The domain of relation D is {2, 3, 12, 16, 27, 48}. For x, y in the domain, xDy if y is an integer multiple of x. (d) The domain for the relation A is the set {2, 5, 7, 8, 11}. For x, y in the domain, xAy if |x-y| is less than 2
- The reflexive and transitive closure of the relation A = {(0,1),(1,2)} on B = {0,1,2} is {(0,1),(1,0),(1,2),(2,1)} {(0,0),(1,1),(2,2)} {(0,1), (1,2)} {(0,1),(0,2),(1,2)} {(0,2)} {(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2)} {(0,0),(0,1),(0,2),(1,1),(1,2),(2,2)}Let R1 and R2 be the relations on {1, 2, 3, 4} given by 6. R, = {(1,1), (1,2), (3,4), (4,2)} R, = {(1,1), (2,1), (3,1), (4,4), (2,2)}. (i) List the elements of R, R, and R, UR,. (ii) Represent digraphs for R1 and R2.3. Given a relation R( A, B, C, D) where FDs ans CKs are such : FDs CKs AB -> C, BC -> D, CD -> A АB and BC А -> ВCD, C ->A A,C А->вс, С->BD, В->А No Clue Check the Highest Normal Form.
- Let A={1,2,3} and B={4,5,6}. The set X={(1,4),(3,6),(2,4),(1,5)} is: O a relation between from A to B, but NOT a function from A to B O a set that has nothing to with A and B O equal to AxB O a function from A to B4. Consider fuzzy relations: yı y2 X1,0.7 0.6 R= x2' 0.8 0.3 Z1 Z2 Z3 Yı [0.8 0.5 0.4 1 2- y2 lo.1 0.6 0.7! Find the relation T = R • S using max-min composition and max-product composition. 6. Find max-average composition for R1 (x, y) and R2 (x, y) defined by the following relational matrices:- 0.9 0.3 0.4 0.1 0.2 0 1 0.7 0.2 1 0.8 R 0.3 0.5 0 0.2 R2 0.8 0.7 0.8 0 1 0.4 0.3 0.4 0.2 0.3 1 0.8 7. For each of the following relation on single set state whether the relation is reflexive, symmetric and/or transitive :- "is a sibling of “ "is parent of “ a) "is smarter than “ “is the same weight as" "is at least as tall as"List all 3-tuples in the relation {(a,b,c)| abc = 6} where a, b and c are all positive integers.