d) Give an example of a relation that antisymetric. Your text defines antisymmetric as "A relation R on a set A is an antisymmetric relation provided that for all X,y EA if xRy and y Rx then x = y. Use A = {1, 2, 3}.

Q: Let R be a relation that is symmetric and antisymmetric. Show that R is transitive

A: Let R be the relation which is symmetric and Anti-symmetric.We will show that R is transitive, that…

Q: Which of the following relations on the set A = {0, 1, 2, 3} is an equivalence relation? Check all…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 4. Let f : X → Y define a relation on the set X by „Ry if and only if (x) = fy). Is f an equivalence…

A: f is an equivalence relation if f satisfies three properties. 1. if f is a reflexive relation  2. if…

Q: If R ={ (1, 2), (1, 4), (2, 3), (3, 1), (4, 2)} is a relation on {1, 2, 3, 4}. Find the reflexive…

A:

Q: Let a relation S be defined on A = {0, 1, 2, 3} as follows. S= {(0, 0), (0, 3), (1, 0), (1, 2), (2,…

A:

Q: Let R be a relation on Z defined by (x,y)ER if and only if 5(x-y)=0. Formall state what it means for…

A:

Q: 1. Show that which of these relations on the set of all functions on Z→Z are equivalence relations?…

A:

Q: B and let R = {(x, y) E A x A | g(x) = g(v)}. Suppose g: A Show that R is an equivalence relation on…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: Let R be a relation on the set A of ordered pairs of positive integersdefined by (x, y) R (u, v) if…

A: Given:

Q: Let - be the relation on R\{0} given by x ~ y if and only if xy is positive. Prove that this is an…

A:

Q: Let R be a relation on the set A = {x € Z:1 < x < 100} defined as follows: x R y if and only if x-y…

A: Equivalence relation

Q: If a relation R on a set A is antisymmetric, then R is not symmetric.

A: To determine whether the given statement is true or false.

Q: 5. Suppose R is a relation on a set A. The inverse relation R-1 is defined by letting a R-1 b if b R…

A:

Q: 8. Define a relation R on the set J = {0, 1,3,4,5,6} as follows: For all x, y EJ, x Ry ⇒ 4x² + y².…

A:

Q: Let R be the relation defined by x R y x² < y² Determine if R is an order relation on N? on Z?…

A:

Q: (i) Let A = {1,2,3,4,5), then either find a relation on A that is not reflexive on A and not…

A: Solution:

Q: a Define a relation R on N by (a,b) e Rif and only if EN Which of the following properties does R…

A:

Q: (b) Let - be the relation on C defined by z ~ w if and only if z + w e R. Proye that is an…

A: This can be solved as follows:

Q: True or False? Let R be an equivalence relation on A = {w, x, y, z}. If wRx, yRz, and wRz, then…

A:

Q: Give an example of a nonempty relation R on A = {1, 2, 3, 4} which is a. symmetric and transitive…

A:

Q: Let H be the set of all human beings. Consider the relation R defined on H by xRy if and only if x…

A: R defined on H by xRy if and only if x and y have the same biological mother. reflexivity : x &amp;…

Q: Let R be a relation on Z. Then Ris an equivalence relation if it is defined by xRy if and only if…

A: R is an equivalent relation iff R is reflexive. R is symmetric. R is transitive.

Q: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…

A: Given a relation R is called atransitive if aRb and bRc⇒cRa Now shows in the following that R is…

Q: Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3,…

A:

Q: 1) Let R be the relation on Z+ such that (p, q) R(r, s) if and only if p- s = q ·r. That is, the…

A:

Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

A:

Q: b) Let S = { (x, y) | x, y € R} and relation R on S defined by (x,y) R (p,q) if and only if x-p =…

A: We have S=x,yx,y∈R x,yRp,q  if and only if x-p=y-q   Reflexive property: A relation R is said to be…

Q: Define a relation C from R to R as follows: For any (x,y) R x R, (x,y)C meaning that x2 + y2 = 1…

A: Given

Q: Define a relation R on Z by xRy → x = y + 5k for k E Z. Prove that R is an equivalence relation by…

A:

Q: Prove whether the following statements are true or false: b) The relation R defined by xRy7[(x-y)…

A:

Q: . Define a relation on R²\{(0,0)} by letting (x₁, y₁)~(x₂,Y₂) if there exists a nonzero real number…

A:

Q: Let G = (V, E) be a graph. Define a relation R on V ly: for all v, y EV, we have v, Rvy if and only…

A:

Q: B Let A = {(x,y) |x-yeQ for x, y = R} be a relation on K. Which statement best describes problem?…

A:

Q: 2. There is a function f : X →Y . Let's define a relation R in a set X, by a formula: (xRy) → (f(x)…

A: Given f: X → Y and R is the relation in the set X such that x R y ⇔ f(x) = f(y)

Q: Consider the relation on Z × Z given by aRb if a &lt; b. Is R transitive. Answer yes or no…

A:

Q: Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r,…

A: (a) Obtain the composite relation as follows.

Q: 4|(x+3y)

A:

Q: Q3. Let R be a relation on the set A = {1,2,3}, defined as follows: R = {(1,1), (1,2), (1,3), (2,…

A: We have to choose the correct option on the given relation.

Q: Provide a rule to define a relation R on N that is reflexive and transitive but not symmetric. Prove…

A:

Q: RUR and RNR symmetric relations on X. are Show that R=Z xZ is an equivalence relation.

A:

Q: (a) Explain what it means for a relation R on a set S to be (i) reflexive; (ii) symmetric; (iii)…

A:

Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

A:

Q: Let R be a relation from set A to B, if R is symmetric then its inverse will be...... Answer (Please…

A: Given R is a relation from set A to B. Let R is symmetric relation and R-1 be the inverse relation…

Q: Give examples of relations R and S on Z such that  Both R and S are not equivalence relations but R…

A: We need to find two set which are on equivalence on Z but their sum do.  LEet, R= a&lt;b S=a&gt;b…

Q: 40

A: By using the definition of equivalence relation solution is given as follows :

Q: Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3,…

A: Equvalence RelationA relation is said to be equivalence relation is it is neflexive, symmetric &amp;…

Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

A: Given: Let A be a non-empty set let~ be a relation on ℘(A) Let "A" be a non-empty set Let ~ be a…

Q: 3. Let L be the collection of all lines in the plane. Define a relation on L by saying that two…

A: Given that L is the collection of lines in a plane. We need to prove the relation defined by two…

Q: (a) Let R be the relation on Z defined as follows: For a, b e Z, a~b if and only if a is a multiple…

A: