Create (a) the ordered pairs, (b) graphical representation, and (c) the relation matrix, for  the Relation R ‘is a factor of’, on set B{1,2,3,6}. (d) Classify the relation R as reflexive, irreflexive, symmetric, antisymmetric, or  transitive.

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: Let x1, x2, y1, y2 be real numbers. The expression (x1, y1) ~ (x2, y2) means that x12 + y12 = x22 +…

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Q: a. Verify reflexive property on the relation R;= {(1, 1), (1, 2), (2, 2), (3, 3), (3, 4), (4, 4),…

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Q: For the relation R closure of R. {(1,2), (1,4), (3,3), (4, 1)} find (i) R2 (ii) R3 and (iii)…

A: The given relation,

Q: Let A = {x, y, z}. Write down a relation R on A that is not reflexive, not sym- metric, and not…

A:

Q: Label the relations below as reflexive (or not), symmetric (or not), antisymmetric (or not), and…

A: A) ONLY antisymmetric

Q: disprove: a relation that is symmetric and transitive must TProve also be reflexive. or

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Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: Let f : A → B be an injective function, a be an order relation on B and 3-1 = {(x, y) E A x A :…

A: An order relation means the criterion of comparison between objects, that satisfies the properties…

Q: 15- R {(x,y) EZ XZI(y-x) = even element} is an symmetric %3D 16- R {(x,y) EZXZI(y-x) = even element}…

A: Recall: Reflexive, symmetry and Transitivity:   Let R be a binary relation on a set A. R is…

Q: Check whether R is reflexive, symmetric or transitive and hence determine whether the relation R is…

A: Reflexivity: Since x≠x+2 , therefore, (x,x)∉R and hence R is not reflexive.   Symmetricity: Let…

Q: The relation p = ((a, b) e R x R: 1+ ab > 0} is %3D (a) reflexive, symmetric but not transitive. (b)…

A: Given relation is ρ =  a, b ∈ ℝ × ℝ : 1 + ab > 0

Q: 1) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x', y')…

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Q: If R is reflexive, symmetric and transitive then the relation is said to be--------

A: Any relation R on a set S is equivalent if and only if it follows the below conditions: (a) R is…

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

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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…

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Q: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

Q: For each relation F, indicate if it is: reflexive, anti-reflexive, or neither; symmetric, anti-…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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Q: Assume (r1, y1) ~ (x2, Y2) → f(x1,Y1) = f(x2, Y2). Prove that ~ an equivalence relation.

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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: We have: The relation is: R=a,c,b,a,c,d,d,b

Q: Q5) Let X = {a, b,c, d} and let R = { (a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (b, d), (d,…

A: Given : X = a, b, c, d R = a, a, a, b, a, c, b, a, b, b, b, c, b, d, d, d be a relation.   To show…

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows:…

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

A: Solution is below provided

Q: Draw the shape of relation z - V3e Зе V3.

A: We are given the relation : z-3eiπ3=3---(1) Now, Let, z=x+iy---(2) Now, 3eiπ3=3cosπ3+i…

Q: Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or…

A: The given relation R is defined as follows.

Q: Describe the equivalence classes of the relation R = {(a, b) : a E Z,beZ, 13 divides (a - b)}

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Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is: %3D (a) reflexive and symmetric…

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Q: 2|A:k||2|| Bx:||2) < || |||B||F k%3D1

A: Please check the answer in next step

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X:V1)< (x2,…

A: The relation ≺ is defined as follows:  x1,y1≺x2,y2 if and only if x1&lt;x2 or x1=x2 and y1≤y2

Q: Α) Reflexive (No), symmetric (No), transistive (No) Reflexive (Yes), symmetric (Yes), transistive…

A:

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: Let A={a,b,c,d} and let R={(a,b)(b,c)(c,d)(d,b)} be a relation on A. Represent the relation using…

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

Q: 4. Let the relation R = { (a, b) e Z × Z l(a + b) = 1 (mod 5) }. a. Is the relation transitive?…

A: A relation R between two sets A and B is the set of all ordered pairs a,b such that a∈A and b∈B. We…

Q: 3.7 Consider a fuzzy relation R CAXA where A = {a, b, c}. R a b e 1 1 1 1 1 1 d 1 1 1 a) Determine…

A: Solution :-

Q: 11. ( a) b) c) [1 1 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 0 1 1…

A: 11. Consider the relation on A = {1, 2, 3} represented by the matrix 111010011   (a) To determine:…

Q: Define a relation R on the x-y plane as follows: Given two points (x1 ,y1) and (x2 ,y2) in the x-y…

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Q: 4- The orthogonal relation is A: symmetric and reflective relation B: symmetric and not reflective…

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Q: Consider the mapping diagram of the relation R below. 2. 3 a) State a counterexample from the…

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Q: Determine whether the following relation is an equivalence relation or not. (a) G = {(x, y) |æ…

A: We have to determine whether the given relation is equivalence relation or not.

Q: Is this relation

A: Using definition of relation

Q: 2. A relation p is defined on the set of all real numbers R by xpy if and only if |x-yl s y, for x,y…

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Q: Define a relation on Z x Z, xRy, |x - y| < 1. Is R reflexive, symmetric, and/or transitive? Explain…

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Q: 11./ a) b) c) 1 1 1 ) Consider the relation on A={1,2,3) represented by the matrix 0 10 1 Determine…

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Q: 1. Consider the relation R1 : R2 - R² such that (r1, y1)R1 (x2, y2) if and only if both points are…

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Q: 11. ( a) b) c) ) Consider the relation on 4= {1,2,3) represented by the matrix 0 Determine if the…

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Q: Which of the following is not a property of a partial ordering relation? O Reflexivity Symmetry…

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Q: Let R be a relation and S its reverse. Show that R is injective if and only if S is well defined,…

A: Consider the provided question, Given that, R be a relation and S its reverse. Let R is a relation…

Q: The adjacency matrix for the relation R on {v1, v2, v3, V4} is given below. 1 0 1 1 0 0 1 1 1 1 1 1…

A: Given the adjacency matrix for the relation R on the set A=v1, v2, v3, v4 as,…