For example, let A = {1, 2, 3} then Cartesian product A × A = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}. A binary relation R ⊆ A × A Briefly explain the meaning of the following relation, providing an example (and diagram) in each case: (i)Reflexive (ii) Symmetric (iii) Transitive

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

A:

Q: Write a computer algorithm, in pseudocode, to test whether a relation R defined on a finite set A is…

A:

Q: For function f from {a, b, c, d} to {1, 2, 3, 4, 5}. f(a) = 4, f(b) = 5, f(c) = 1 and f(d) = 3, The…

A: - We have to get the domain of the set where function is called from {a, b, c, d} to {1, 2, 3, 4,…

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: Given a set A = {1, 2, 3, 4}, which of the following relations is a partial order relation and which…

A: In this question we have been given some relations and we need to determine which relations are…

Q: p.629, icon at Example 2 # 1. Let R be the relation on {1,2, 3, 4} such that R = {(1, 1), (1, 4),…

A: Step 1: Step 2:

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: Consider the issue of interesting orders in optimization. Suppose you are given a query that…

A: The interesting order is every order on the subsets of the attributes which can potentially take…

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: Define a relation S on B={a,b,c,d} by S={(a,b),(a,c),(b,c),(d,d)}. Draw the directed graph of…

A:

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

A: Answer is in step 2

Q: Draw a directed graph for that partial order relation that is defined on a definite set that…

A: Let us draw the directed graph for the partial order relation for the power set.  The power set of…

Q: Given the relations U and S below, use ordered pair notation to express the relation So U. a b b

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

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: 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: The binary relation {(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2)} on the set {1, 2, 3} is…

A: Option ATransitive.

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: A = {0, 1, 2, 3} and let R be a relation on A such that xRy if and only if x List the elements of R.

A: Given A={0,1,2,3}R is a relation on A such that xRy if and only if x-y is odd. The list of odd…

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: Let S be a set with |S| = 5. How many relations are there on S? А. 5! В. 55 С. 520 D. 525 Е. 225

A: There are E. 225 relations on S.

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

A: 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: Let L be a strict subset of LAc (i.e. L c LACC). Then L is ( always / sometimes / never ) decidable.

A: Defined the given statement always, sometimes or never

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

A:

Q: Let Ri and R2 be the relations on (1,2,3,4} given by R1 = {(1,1), (1,2), (3,4), (4,2)} R2 = {(1,1),…

A: we will discuss the composition of the given relation in the next step

Q: Construct the CFG of the given DF

A: All the final state will have e or epsilon as one of the production.

Q: Let A be a non-empty funute set and let S = P(A). Define relation R ⊆ S × S by: xRy ⇔ |x| = |y|,…

A: In this question we have to prove Realtion R is an equivalent relation for the define data and need…

Q: Q5) Consider the following Relation (T) which is a bag(Recall our discussion about bags an sets) P 1…

A: Relational Algebra which refers to the one it is a procedural query language which also it takes 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: Refer to image and answer correctly for upvote! (Automata and Computation)

A: An equivalence relation must satisfy three properties:1. Reflexivity: Every element is related to…