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: Suppose ρ is the relation defined on P({1, 2, 3}) in which, for A, B ∈ P({1, 2, 3}), AρB means "A…

A: Given: P({1, 2, 3}) A, B ∈ P({1, 2, 3}) AρB means "A and B both have exactly 2 elements."  ρ is…

Q: 3. Given a relation R( A, B, C, D) where FDs ans CKs are such : FDs AB -> C, BC -> D, CD -> A CKs АB…

A: Here in this question we have given a relation R and we have asked to check highest normal form in…

Q: Consider the relation r(A,B ) with the following instance of r. Which of the functional dependencies…

A: Rules to check valid functional dependency from   α -> β   Check if all the values of α are…

Q: Consider the relation R defined on the set Z x Z: R = {((a,b),(c,d)) | a = c (mod 4) a b = d (mod…

A: given that

Q: Consider the set of F of the following functional dependencies on relation R(A, B, C, D, E): AB C…

A:

Q: Let R be a relation on A = {0, 2, 7, 8} and R = {(7, 2), (8, 8), (8,0), (2, 7), (2, 2), (7,0)}. Are…

A: The given relation R is defined on the set A = {0, 2, 7, 8}, and R = {(7, 2), (8, 8), (8, 0), (2,…

Q: • Let A be the set A={a,b,c,d} and R is a relation on set A, where R= { (a,a), (a,b) ,(b,a),(b,b),…

A: A = {a,b,c,d} R= {(a,a),(b,a),(b,b),(c,d),(c,c),(d,d)}

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: Given: Relation R = {(a,c), (b,c), (c,c)} and Set S = {a, b, c} %3D Complete Relation R to be…

A: Given: To make the relation R symmetric.

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: 3. R is a binary relation over N, the set of natural integers. (x, y) € R iff x mod 7 = y mod 7. R…

A: Binary Relation:A binary relation is a mathematical concept that defines a relationship between two…

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: Let R be a relation on A = (0, 1,7,9). If (7,9) ER, what must NOT be an element of R for R to be…

A: Let R be a relation on A = {0, 1,7,9). If (7,9) ER, what must NOT be an element of R for R to be…

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: Consider the following Relation instance of R1(A, B, C, D): A D Null Null 1 Null Null 1 1 Null 1 2 4…

A: A relation stores data about entities using database languages. The structure of a relation is…

Q: Let FD ={G → A, A → BC, C → FG, E → HG} be a set of functional dependencies. Calculate the…

A:

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: Oa.2

A: Here as we can see all vertices have self loop. Thus the relation is = .  Also as we can see there…

Q: Suppose relation R is defined as two-dimensional matrix A. Give a pseudo-code for transitive…

A: A)THE BELOW ANSWER IS FOR BOTH PARTS IN THE QUESTION: #include &lt;bits/stdc++.h&gt;using namespace…

Q: Which of these FDs hold on the

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

Q: Suppose that we decompose the schema R = (A, B, C, D, E) into (A, B, C) (A, D, E). Show that this…

A: SOLUTION -   Given Relation R = (A,B,C,D,E) and dependencies are A --&gt; BC CD --&gt; E B--&gt;D…

Q: er the questions

A:

Q: let S = {s1, s2, s3, s4, s5}. Give an example of an equivalence relation R on S such that S/R has…

A: Answer :-)

Q: Let S = {1,2,3}. Let be the relation on Sx S defined by (a, b) ≤ (c,d) a ≤ c and b>d (a) Show that…

A:

Q: e. R is a relation on ZxZZ such that ((a, b), (c, d)) ER if and only if a+b>c+d.

A: In mathematics, relations play a crucial role in understanding the interactions between elements of…

Q: Let S be set of all strings of a's and b's. Define a relation R on S as follows: Vs,t E S, sRt +…

A: Given: s, t are elements of S.

Q: Answer with a YES or NO. Given a relation R on set A={1,2,3,4}, such that aRb if and only if a + b.…

A:

Q: 2.Consider relation R=(A,B,C,D) with the following FDs: B → C, C → D, and D → A a. List all…

A: 2. Given, Relation is R = (A, B, C, D) The set of functional dependencies given is :  B -&gt; C C…

Q: Let R1, R2,…, Rn be a decomposition of schema U. Let u(U) be a relation, andlet ri = ΠRI(u). Show…

A: Given,  R1, R2,…, Rn be a decomposition of schema U u(U) is a relation ri = ΠRI

Q: Given: Relation R = {(a,a), (a.b), (b,a). (b,b). (c,c)} and Set S = {a, b, c} Complete Relation R…

A: Find the answer given as below :

Q: Given set A={1,2,3,4,5} and let R and S be a binary relation on set A. R = {(a, b) e AxA | b|a} and…

A:

Q: Consider the relation R on Z? given by: R= {((a,b), (c, d)) : a + d = c+ b} Prove that R is an…

A: Z denotes set of all integers {....,-3,-2,-1,0,1,2,...} i.e, both positive and negative. So, Z2…

Q: Let R be a relation on A = {0, 1, 6, 8} and R = {(0, 0), (8, 6), (6, 6), (8, 8), (1, 1), (1, 0), (0,…

A: 1. R is symmetric Answer: False Explanation:  because of (8,6) ∈ R, but (6,8) ∉ R.   2. R is…

Q: Consider a relation schema R(A,B,C,D,E,H,G)   F = {A->BC, B->C, C->BED, BD-> E, E->D, AG->E, G->H,…

A: Answer is given below-