Let A = {1, 2, 3, 4}. Give an example of a relation on A that is: %3D (a) reflexive and symmetric but not transitive. (b) reflexive and transitive but not symmetric. (c) symmetric and transitive but not reflexive. (d) reflexive but neither symmetric nor transitive.

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

A: A) ONLY antisymmetric

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

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Q: Suppose that R1 and R2 are symmetric relations on a set A. a) Is R1 U R2 also reflexive? Is R1 ∩ R2…

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Q: Given a relation, R on A = {a, b, c, d} on as follows: R = {(а, а), (а, b), (а, d), (b, b), (b, с),…

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Q: consider the relation ∼R on P(N), the power set of N, with A  ∼R B iff A∩B ≠ ∅ determine whether…

A: consider the relation ∼R on P(N), the power set of N, with A  ∼R B iff A∩B ≠ ∅

Q: Let R be the relation on the set of ordered pairs of positive integers such that  ((?, ?), (?, ?)) ∈…

A:

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 the relation S defined as S = {(x,y) | y = X2 + 4x +3}. What is the domain of S?

A:

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…

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

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Q: Every function is a relation of its domain and codomain. O True. O False.

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Q: Let A = {a, b, c}. a) Give an example of a relation on A that is reflexive and symmetric, but is not…

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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: let R be the relation on the set of positive integers in which a R b if and only if a is a factor of…

A: Given below the detailed Solution.

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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…

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Q: Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric,…

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Q: Q3. Let A = {n| 3<n< 30} and define a relation on A such that aRb iff (a + 1) | b. i. List the…

A: Hi! We are solving only (i) and (ii). As the other parts are lengthy, kindly re-post the question by…

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Q: A relation R is defined on the sets of integers by aRba2+b2=(a+b)2-2ab Show that R is symmetric

A: A relation is called symmetric if aRb⇔a2+b2=(a+b)2-2ab

Q: (c) The reversed relation R is an equivalence relation. (d) So R is an equivalence relation if and…

A: (c) If R is an equivalence relation in a set X, then it is reflexive, symmetric and transitive.

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…

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A: Reflexive: (x,y) R (x,y) As x+y=x+y Symmetric : if (a,b)R(c,d) then a+b=c+d. Since c+d=a+b then…

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Q: Exercise 19. Let R be the relation given by the following digraph. Then (2)- a. (1.2.3) b. (1.3) c.…

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Q: A partial order relation is that which is A Reflexive, symmetric and transitive B Reflexive and…

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Q: y if and only if x < 3y. Determine, plem B4: Consider the relation ~ on N defined by, x ~ proof,…

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

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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: 3. Let R be the relation defined by x R y + x² <y? Determine ifR is an order relation on N? on Z?…

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Q: Suppose you have the following relation: R: A-A where A = (a, b, c, d, e) %3D R= ( (a, b), (a, e),…

A: Given relation is R:A-&gt;A where A={a,b,c,d,e}R={(a,b)  , (a,e) , (b,e) }determine whether it is…

Q: 5) Let R be the relation on the integers where a Rb means a² = b². a) Is this an equivalence…

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Q: Write A here: A =. Let R be the relation on {0, 1, 2,3, 4, 5, 6, 7,8, 9} given by: (0,0), (0, 1),…

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A: Given

Q: Which of the following are examples of an equivalence relation on Z? Select all that apply. A. a ~…

A: Hence the relation is an equivalence relation.

Q: let A= {a,b,c,d} and R= {(a,a),(a,c),(b,d),(c,a),(c,c),(d,b)} be a relation on A. What is the…

A:

Q: Give an example of a relation. Which is(i) Symmetric but neither reflexive nor transitive.(ii)…

A: i. Symmetric but neither reflexive nor transitive.