Question 13 For each relation: (1) antisymmetric, and transitive (for transitivity just show two examples). (2) Show whether or not the relation is reflexive, symmetric, State whether it is or is not an equivalence relation. (a) R={(a,a), (b,b), (c,c), (a,b), (a,c), (c,a), (b,c), (c,b)}

Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

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Q: (b) Define Equivalence Relation with an example. Give an example of a relation which is not…

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Q: 7. (6 points) Let T be a relation defined on the set A = {1,2,3} such that T = {(1,1), (1,2), (2,2),…

A: The objective of the question is to determine whether the given relation T is reflexive, transitive,…

Q: The inverse of a relation r is r {(0, 0), (0, 1), (0, 2) }. Which of the following may be the…

A: Topic = Relation   The Inverse of a Relation is a set of ordered pairs that is the exact inverse of…

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A: Given:-               A car dealership sells cars that were made in 2015 through 2020. Let the cars…

Q: How many (distinct) equivalence classes does the relation R-(1.1), (2.2) (3,3),(4,4), (1,2), (2.1).…

A: The relation is R=1,1,2,2,3,3,4,4,1,22,1,3,4,4,3 The set is X=1,2,3,4

Q: Let A = {1,2, 3,4,5,6,7,8,9} and R be a relation in A ×A, defined by (a, b) R(c, d) → a + d = b + c…

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Q: 22) (a) Show that the relation {(0,0), (1,1),(1,2), (2,1), (2,2), (3,3)} is an equivalence relation…

A: Given 0,0,1,1,1,2,2,1,2,2,3,2

Q: Given the relation R = {(1,2),(2,3)} on the set A = {1,2,3} . What is the minimum  number of ordered…

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Q: let S be the set of all dogs, and define the relation R on S such that (a, b) = R if b and a have…

A: Reflexive: A relation R is reflexive, if for every element 'a' in S, (a, a) belongs to R. In this…

Q: Create (a) the ordered pairs, (b) graphical representation, and (c) the relation matrix, for  the…

A: Given a relation R on the set B as "is factor of" B=1,2,3,6. a The ordered pair is…

Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Consider the following relation on {1,2,3,4}. Check is equivalence or not? R= {(1, 1), (1, 2), (2,…

A: Follow next step

Q: 4. Let X be any finite set and define the relation R on P(X) by R= {(E,F)||E| = |F\, E, F € P(X)}.

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Q: Please show the following question in detail, I don't understand one bit of it, " Let R be a…

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Q: QUESTION 2 Define a relation on Nx N as follows: (a, b) R (c,d) a+d=b+c (2.1) Is (3,6) R (3,5)?…

A: We have to show that the given relation is an equivalence relation.

Q: Determine whether the relation is reflexive, symmetric, antisymmetric and transitive. Provide one…

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Q: 4. For each relation R below, determine whether it is an equivalence relation on the given set A.…

A: Definition (Equivalence relation): A relation R is said to be an equivalence relation on a set A if…

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Q: a) Relation R is defined on Z as follows: for every a, b € Z, a R bif 4 | (a - b) (i.e., 4 divides…

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Q: (d) Let x be the complex number 1-i. Use de Moivre's Theorem to find the smallest n E N such that x"…

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Q: Indicate which of the following relations is an equivalence relation or is a partial order relation.…

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Q: True/False: The relation R = {(a, a), (a, b), (b, a), (b, b), (c, c), (a, c), (b, c), (c, b), (d,…

A: The given set is                         S = { a , b , c , d }  and the given relation is…

Q: For each relation R below, determine whether it is an equivalence relation on the given set A. Also,…

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Q: Please help me with this question. I don't understand what I did wrong. Please kindly input the…

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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: Consider the following relations R1, R2, R3, R4 on the set [4] = {1,2, 3, 4}. Each of the relations…

A: Here we use definition of function and relation

Q: (a) Consider the relation R on the set A = {p, q, r, s} defined by R= {(p,p), (p, q), (q, r), (r,…

A: (a) R is a relation on the set A = {p, q, r, s}       R = {(p, p), (p, q), (q, r), (r, s), (r, r),…