1. Consider the relation R on the set (a,b.c,d,e,f] which is defined as follows: R-[(a,a), (a,b). (a,c). (b.a). (b.c), (c.a). (c.b). (d.d), (f,f). Is R reflexive? Is R symmetric? Is R anti-symmetric? Is R transitive? Give reasons

Q: Define two sets: a letter set A = {t. p. c) and a word set B = {proposition, math, proof, discrete).…

A:

Q: Which of the followings can possibly be a canonical cover Fc of a set F of functional dependencies?…

A: The answer to this question is option b) {A → D, AB → C, D → B} and d) {A → C, D → B, AB → C}

Q: Given the relation U below, use ordered pair notation to express the relation U o U. U o U = { Ex:…

A: To express the relation UoU (composition of relations U and U), find all pairs (x, y) such that…

Q: Let R be a relation on A = {0, 2, 3, 7} and R = {(7,7), (3, 3), (0, 2), (2, 0), (2, 2), (0, 0)}. Are…

A: SOLUTION- Given, A ={0,2,37} and R={(7,7),(3,3),(0,2),(2,0),(2,2),(0,0)} 1)True  A  relation R…

Q: 3. Suppose the relation R1(A,B) and R2(B,C,D) have the following tuples: A 1 7 2 4 9 B A T G C T B…

A: A theta join connects tables based on a relationship other than the equality of two columns. A theta…

Q: ;; "relate" accepts a positive integer x and relation R and returns { y | (x y) €R }. ;; Type…

A: Helper Function : An helper function is a capacity that performs part of the calculation of another…

Q: Q # 3; (a). The relation ‘R’ is defined on the set M=(4,5,6,7) as the following;…

A: Given the relation R on M =(4,5,6,7) and given relation is R={(5,5),(5,6),(5,7),(6,5),(6,6),(6,7)}…

Q: Consider a schema R, a set F of functional dependencies on R, and two candidate keys (k1, k2) as…

A: Given information: - R is schema in which F is a set of functional dependencies two candidate keys…

Q: Given two sequences A and B. Let X(A, B) denote the number of times that A appears as subsequence of…

A: The first option is the correct choice. Find teh code implementation below.

Q: Consider the relation R(S, N, R, C, J, H, L) and its set of dependencies F = {S, N -> C ; J, H, C ->…

A: using Armstrong's axioms=> proved in figure figure 1:

Q: 4. Consider again the structure R = (IR, +, x, <) and let P(x, y) be the predicate a < y. Express…

A: The solution for the above given question is given below:

Q: Given set A = {a, b, c, d} show the equivalence relation, which contains eight ordered pairs,…

A: Answer is in step 2

Q: Define a recurrence relation T(n) that corresponds to the natural numbers, but that "skips"…

A: A recurrence relation is an equation that recursively defines a sequence where the next term is a…

Q: 1. The Fibonacci numbers F(0), F(1), F(2), are defined by the recurrence relation: F(0) = 0,…

A: The complete Handwritten answer is solved below:

Q: G= ({S, A, B, C}, {a,b,c}, S, P) where P S → AB A AB|CB| a BAB b CAC C

A: NPDA stands for non-deterministic pushdown automaton. It is basically a type of computational model…

Q: 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…

A:

Q: Consider a relation T on Z where T = (1,1)}. Is T reflexive? Is T symmetric? Is T transitive?…

A: Given a relation T on Z T={(1,1)}   T is not reflexive because Z is integer and has many element so…

Q: b) Express the following relation using a set-builder notation R = {(1, 2), (2, 6), (3, 9), (4, 16),…

A: Set-builder notation is a mathematical notation for describing a set of representations.

Q: For example, let A = {1, 2, 3} then Cartesian product A × A = {(1,1), (1,2), (1,3), (2,1), (2,2),…

A: Brief explanation about Reflexive, Symmetric and Transitive is presented here:-

Q: For non empty binary relation R={(a, a).(a, b),(b, a).(b, b).(c, C).(C, d).(d, C).(d, d)} on the set…

A:

Q: Let R be the relation R = {(a, b) | a < b} on the set of integers. Find a) R-!. b) R.

A: a)R-1

Q: The relation x ≡ y if and only if x mod 4 == y mod 4 is an equivalence relation. Use this…

A: A.

Q: Q6) Let A = Z, the set of all positive integers, and we define the relation R on A as: a Rb if and…

A:

Q: Let A equal the set of all strings of 0's, 1's, and 2's that have length 4 and for which the sum of…

A: A = { 0000, 1000, 0100, 0010, 0001,            1100, 1010,  1001, 0110, 0101,            0011, 2000,…

Q: Consider a schema R and a set F of functional dependencies as follows: R= (A,B,C,D,E,G). F = {A →…

A: First of  all , let’s understand what is super key.      Super key : Super key can be defined as  an…

Q: Normalization Here is a set of FDs for a relation R {A, B, C, D, E, F, G}; AB BC>DE AEF>G AC>DE a.…

A: Given, Relation schema = ( A, B, C, D, E, F, G ) The set of functional dependencies are : A -&gt; B…

Q: Can renaming be pushed through join and selection—that is, which of the following algebraic laws…

A: SUMMARY: -   Hence we discussed all the points.

Q: The reflexive and transitive closure of the relation A = {(0,1),(1,2)} on B = {0,1,2} is…

A: Here in this question we have given a relation on some set B. and we have asked to find the…

Q: 2. Given the sets A = {1,2,42}, B = {24,7,1,2}, provide a brief description (prose) and list the…

A:

Q: Which of these FDs hold on the

A: Functional dependency: The columns of a relational table are functionally dependent on another…

Q: er the questions

A:

Q: Consider the relation R = {(a, d), (b, a), (b, c), (c, b), (c, c), (d, a)} on the set {a, b, c, d}.…

A: Below are the required answers :

Q: Define a relation R on Z×Z by (m,n)R(s,t) if and only if m-n = s-t. Is R reflexive? symmetric?…

A: In the given case, we prove all three one by one.

Q: finite; a partial order on K such that, for all pairs x, y € K satisfying y and ry, the condition y…

A: A total order on K such that, for all pairs x, y € K satisfying both and x &gt; y, the condition y…

Q: I. Reflexive II. Symmetric I. Transitive IV. Antisymmetric For each of the following tvpes of…

A: - The question wants to know that what categories fell under the partial , total and equivalence…