In each case below, a relation on the set {1, 2, 3} is given. Of the three properties, reflexivity, symmetry, and transitivity, determine which ones the relation has. Give reasons. (a) R = {(1, 3), (3, 1), (2, 2)} (b) R = {(1, 1), (2, 2), (3, 3). (1, 2)} (c) R=Ø

Q: Let A = {3,4,5,6,7,8} and define a relation R on A as follows: For every x, y E A, x R y + 2|(x –…

A: The arrows between two numbers or the number and itself must differ by a multiple of 2 ie, 0,2,4,6,8…

Q: A relation Ron A is an equivalence relation if it is reflexive, symmetric, and transitive. Given: A…

A:

Q: Determine the following for the given relation R on the set { 1, 2, 3, 4, 5, 6 } defined by the rule…

A:

Q: For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, symmetric,…

A: The Reflexive Property states that for every real number x,x=x x , x=x . Symmetric Property. The…

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9} and let R be the relation {(a,b) ! a , b} Find the smallest…

A:

Q: {a,b, c, d} which is symmetric and (a) Give an transitive, but not reflexive. example of a relation…

A: a) Definition of symmetric, transitive, reflexive relation: Let, R be a relation on A. R is said to…

Q: Let A = {2, 3, 4, 6, 7, 9} and define a relation R on A as follows: For all x, y e A , x R y = 3…

A: Given A = {2,3,4,6,7,9} xRy ⇔ 3 divides (x-y) Therefore 1)  R = (2,2) , (3,3) , (4,4) , (6,6) ,…

Q: ' (a,b) ∼ (c,d) ⇔ a+d =b+c '' defined as '∼' relation is that a equivalence relation?

A: It is equivalence relation if (a, b) belongs to ZxZ

Q: 2. Identify which is a relation and a function. a. U = {(-1,1), (0, 1), (1,1), (2, 1), (3, 1)} b. W…

A:

Q: The domain for the relation R is Z × Z. (a,b) R (c,d) if and only if a <c and b< d. Indicate whether…

A:

Q: For each relation, decide whether or not that relation is reflexive, symmetric, antisymmetric or…

A:

Q: Let R be the relation {(1,2),(1,3),(2,3),(2,4),(3,1)}, and let S be the relation…

A:

Q: Let A= {0,1,2,3,4} and a partition of A be: {0,2},{1},{3,4} (a) Write all pairs of the relation…

A:

Q: 4. Let R and S be relations defined on the set A. If both R and S are symmetric relations, are: a) R…

A:

Q: Which of the following relations is the Symmetric relation over the set A= {3,5,13}…

A:

Q: Which of the following sets of ordered pairs represents a relation that is not a funetion? (1, 1),…

A: We know that set of order pairs like (x,y) forms a relation. Now, when a relation contains a special…

Q: Q2. (a) Find the equivalence class [-3]5 (b) Find the ordered pairs of the relation R from the set A…

A: We have to answer the following questions :  (a) Find the equivalence class  -35 (b) Find the…

Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: A relation R on a set A with elements a, b and c is said to be in a transitive relationship, then if…

Q: Determine whether the given relation is an equivalent relation on {1,2,3, 4, 5}. If the relation is…

A: Equivalence class of an element a is given by [a] such that [a]={b:(a, b) lies in R}

Q: The range of the relation R = {(x,x²)|x is a prime number less than 13) is a. [2,3,5,7) b.…

A:

Q: Check whether the relation R on the set S = {1, 2, 3} is an equivalent relation where: ? = {(1,1),…

A:

Q: d) Let R be a relation on Z and x R y if x - y is even. e) Let R be a relation on N x N where (a, b)…

A:

Q: Is Ra partially ordered relation ? ? . Why ?..

A: Solution is below provided

Q: A relation is an equivalence relation if it satisfies three properties. which of the following…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: |Given the relation R= {(1,1), (2, 4), (3, 1), (4, 1), (5,2)} on the set A= {1,2,3,4,5), find the…

A: We know: Symmetric closure of a relation R, △, is obtained by adding (b, a) to R for each (a, b) ∈ R…

Q: Construct a relation on the set {1,2,3,4} that is reflexive, antisym- metric, and not transitive.

A:

Q: Define a relation R2 on the set A = {0, 1, 2, 3} as follows.R2 = {(0, 0), (0, 1), (1, 1), (1, 2),…

A:

Q: Suppose that the relation of H is defined as follows. H= {(9,m), (4,0) (5,m)}   give the domain and…

A:

Q: Suppose that the relation T is defined as follows. T = {(2,b), (7,0), (4,2), (7,a)} Give the…

A:

Q: By listing the elements as ordered pairs, define a relation on the set A = {e, 2, 7, ♡} which is:…

A:

Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

Q: For each of these relations on the set {1,2,3,4}, draw the graph of the relation: {(1,1), (2,2),…

A: For each of these relations on the set {1,2,3,4}, to draw the graph of the relation.

Q: Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as follows:…

A: We have to Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as…

Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

A: If R is any symmetric relation on a set A, then R-1 is symmetric.Proof :1. Let R be any symmetric…

Q: For the set A = {are, bot, cab, era)}, define the relation R on A to be: (x,y) eR if and only if…

A: As per the condition, in every order pair there should be only 1 letter in common.

Q: Consider the relation on the set N x N given by (m, n)R(k, l) if m + n = k + l. List three elements…

A:

Q: Let A = {1,2,3, 6}. Define a relation R on A as follows: %3D xRy if y – x > 0 Write out the relation…

A: We have to find the relation R.

Q: The domain for a given relation R is the set A = {1,2,3,4). Select the correct description of the…

A: A relation R on set A is called Anti-Symmetric if xRy and yRx implies x=y∀x∈A and ∀y∈A. Example −…

Q: given the relation R define = (0,0), (0, 1), (0, 3), (1, 1), (1,0), (2, 3), (3, 3) on the set A = 0,…

A: Given that  R=0,0,0,1,0.3,1,1,1,0,2,3,3,3A=0,1,2,3 To draw the directed graph and determine whether…

Q: Let A = {6, 8, 10, 15, 17} and B = {2, 3, 4, 5} and define a relation R: A → B as follows: For all…

A: Given   A = {6, 8, 10, 15, 17};  B = {2, 3, 4, 5}; relation R: A → B  ordered pairs of A and B that…

Q: Given this set of points (1, 10), (3.5, 7), (4, 8), (8, 4), (8, 16), (10, 6). Which points create a…

A:

Q: Let B = {1, 2, 3, 4} and S be the relation defined by S = {(1,1), (1,3), (1,4), (2,2), (2,4), (3,3),…

A: Let B = {1, 2, 3, 4} and S be the relation defined by S = {(1,1), (1,3), (1,4), (2,2), (2,4),(3,3),…

Q: cercise 2. Give an example of a relation R on A = {1,2,3} that is neither reflexive or irreflexive.

A: Given A = {1, 2, 3}

Q: A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain…

A: Given

Q: Let R be the relation {(1,2), (1,3), (2,3), (2,4), (3,1)} and let S be the relation {(2,1), (3,1),…

A:

Q: Let A = {1, 2, 3, 4, 5} Determine whether the relation R whose diagraph is given is relflexive,…

A: A relation R is said to be reflexive on the set A if for every element x in the set A, the ordered…

Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5}. If the relation…

A: