Write a function in python that takes a set A and a relation
R(x, y) on A (as a python function such that R(x, y) returns true
if and only if the relation xRy holds), and returns True if and
only if the relation R is reflexive. Here is the function signature
you need to use.
def is reflexive(A, R): You can test your code as follows. s = {1,2,3} def y(x, y): return x == y def n(x, y):...
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...
3. Let the relation R be defined on the set R by a Rb if a -b is an integer. Is R and equivalence relation? If yes, provide a proof. Consider the equivalence relation in #3. a. What is the equivalence class of 3 for this relation? 1 b. What is the equivalence class of for this relation? 2
Consider the following relation: R(A,B,C,D,E) The following set of functional dependencies are ture on the relation R: FD: AB -> E, E -> D, AD -> C Which of the following sets of attributes does not functionally determine C? AC ABE BD AE AB
(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f is 0(g)" on F is: (a) (4pt) Write down the definition for "f is O(g)". (b) (4pt) Prove that the relation is reflexive (c) (6pt) Prove that the relation is not symmetric. (d) (6pt) Prove that the relation is transitive.
(17) (20pt) Let F be the set of functions f : R+ → R. Prove that the binary relation "f...
10. [4] Let R be the relation on the set {0, {f}, {y}, {x,y}} defined by R= {(S, T): SUT|=2} (a) Represent the relation R as a set of ordered pairs. (b) Represent the relation R as a relational digraph.
Prove that if R is an equivalence relation on a set A, then R ^-1 is an equivalence relation on A.
Question 8
Let R be relation on a set A. 1. When is R said to be an equivalence relation? Give a precise definition, using appropriate quantifiers etc. 2. When is R said to be an partial order? Give a precise definition, using appropriate quantifiers etc (You don't need to redefine things that you defined in the previous part... you may simply mention them to save time.) 3. On Z, define a relation: a D biff a - b is...
Check which of the following options are TRUE for the relation R* The relation R is defined on a set A = {0, 1, 2, 3} as follows: R= {(0,0), (0, 1), (0,3), (1,1), (1,0), (2,3), (3,3)} Anti Symmetric Symmetric ansitive Reflexive
Define the set F- (XI X is a finite set of counting numbers) and the relation is a finiice sei of counting nuobors and the relation {(X Z〉 | Ye F and Z € Fand y-2). This relation is just a version of the usual subset relation, but restricted to only apply to the sets in F Prove: CFis a partial order. Prove: Cis not symmetric and connected. Prove: If R is an equivalence relation, it is also a euclidean...