Show the following rule for MVD's. The attributes are arbitrary sets X, Y, Z and the...
Consider the following definition of equivalent sets of functional dependencies on a relation: “Two sets of functional dependencies F and F’ on a relation R are equivalent if all FD’s in F’ follow from the ones in F, and all the FD’s in F follow from the ones in F’.” Given a relation R(A, B, C) with the following sets of functional dependencies: F1 = {A B, B C}, F2 = {A B, A C}, and...
Consider a relation R with 5 attributes M, O, N, E, Y. You are given the following dependencies: M-> N O -> M Y -> E NM ->Y Its candidate keys are {( O)}. 1. Which of the following is a prime attribute for the relation R? _________________ i.M ii.E ii.O iv. All attributes of the relation R are prime attributes 2. Which of the following is true about the given functional dependencies in the relation R? ______________ i.M ->...
3-4 Points) Let R be an arbitrary ring and z, y R. Show that x2-y- (x +y)(x -y) if and only if R is a commutative ring.
2. Consider an 1NF- relation StudentDB2 (sID, sFName, sLName, cID, cName, cCr, sectID, iID, iTitle, iLName, grade) that satisfies the following five functional dependencies: FD1 {sID}->{sFName, sLName} FD2 {cID}->{cName, cCr} FD3 {cID, sectID}->{iID} FD4 {iID}->{iTitle, iLName} FD5 {sID, cID, sectID}->{grade} a. What is/are candidate key(s) for relation StudentDB2? b. Normalize the relation StudentDB2 into a collection of 2NF-relations. c. Normalize the relation StudentDB2 into a collection of 3NF-relations. d. Normalize the relation StudentDB2 into a...
The grandparent relation can be defined by rule the following way: For all X and Y, X is the grandparent of Y if X is a parent of Z and Z is a parent of Y Write the above relation in prolog
Solve the system in terms of the arbitrary variable listed. Z; x + y + z = 9 2x - 3y + 4z = 7 0 {***} • {2,3,2,0) o {200,- © {{2,3,2,1,1)
X, Y, Z are three sets in a sample space S. Find P(X|Y ∩Z) if P(X|Y ) = 0.1 and P(X|Z) = 0.35 are given.
2. Consider the following transformations of R2 Tİ (z, y) (-r, y), T3(x, y) (z, _y), T,(zw) (y, x). Show that, for any j 1,2,3, a subset A C R2 is a Jordan region if and only if T,(A) is a Jordan region. What is the relation between the volumes of A and T, (A)?
2. Consider the following transformations of R2 Tİ (z, y) (-r, y), T3(x, y) (z, _y), T,(zw) (y, x). Show that, for any j 1,2,3,...
Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over each solid shown & described below. i.e., Fill in the six limits of integration and the blank at the end. There is nothing to evaluate. (a) The solid is between the top hemisphere of the ball of radius 2 centered at the origin and the inside of the upper half cone z = Vx2 + y2. r?+ y2 + = 4...
Cramer's Rule: 5. Use Cramer's Rule to find x,y and z for the following system of equations. X 2 7x + 2y - z= -1 ។ 6x + 5y + z = 16 -5x - 4y + 3z = -5 2 : 2 a. Write the coefficient matrix first for the system above. Call it matrix D. 7 2 5 L-8-4 3 1 14 ] = 0 b. Find the determinant of the coefficient matrix (det(D)).