Determine whether the given relation is reflexive, symmetric, transitive and an equivalence relation. Justify your answers. a) b)

Q: Consider  the relation R={(a, b),(a, c),(c, b),(b, c)} on  the set A={a, b, c}. Is R reflexive? Is R…

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Q: Write an equivalence relation of Set A = {1,2,3,4,5,6}

A: Set A={1,2,3,4,5,6}

Q: 6. Consider the relation R = {(a, b), (a,c), (c, b), (b,c)} on the set A = {a, b,c}. Which of the…

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Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: we have given a set  A = { 1, 2, 3, 4}  and R is a relation on the set A where R is defined as (a,…

Q: Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} asR = {(a, b) : b = a + 1} is…

A: Given, relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1}.

Q: Determine whether the given relation is reflexive, symmetric, transitive and an equivalence…

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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: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

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Q: Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric,…

A: Consider the given information:

Q: Consider the relation R = {(1, 2),(2, 1),(2, 3),(3, 4),(4, 1)} on {1, 2, 3, 4}.Is R reflexive?…

A: In this question we have to explain Is the given relation is reflexive.

Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: 1. Let A = {0,1,2,3,4,5}. Write out the relation R that expresses greater than orequal on A. Then…

A: Handwriting solution

Q: n R m in Z if nm>0

A: 1) reflexive property : for all n in Z - {0}, we have, n R n because, n•n = n² > 0 But, for n = 0…

Q: Let A = {a, b, c, d} and R = {(a, a), (b, a), (b, b), (c, c), (d, c), (d, d)}. Determine whether the…

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Q: Determine the following relation on the set {a, b, c, d}, is reflexive, irreflexive, symmetric,…

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Q: Consider the relation R = {(a, b), (a, c), (c, c), (b, b), (c, b), (b, c)}. Is R reflexive,…

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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: VIII.3. Is there a mistake in the following proof that any transitive and symmetric relation Ris…

A: Yes there is a mistake. That Symmetric and transitive relation doesn’t imply reflexive. in the…

Q: The domain of relation R is ZxZ. (a, b) is related to (c, d) if a s c and b s d. Which statement…

A: In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and…

Q: ii. Determine whether the relation, R = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} is: Yes/No…

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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: Which relation on the set {a, b, c, d} are equivalence relations and contain (i) (b, c) and (c, d)…

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Q: Let R be the relation, {(a, b) e N x N:a + b is odd}. Give an example that shows that R is not…

A: Given R be the relation, {(a, b) ∈ N x N:a + b is odd}.  We find an example that shows that R is not…

Q: The 2-tuples (ordered pairs) of integers is the set Z x Z and can be given an equivalence relation…

A: The given set is ℤ×ℤ, where ℤ is the set of all integers. So basically ℤ×ℤ is the set of all ordered…

Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: Determine the following relation on the set {a, b, c, d}, is reflexive, irreflexive, symmetric,…

A: Let R represent a relation on a given set S=a,b,c,d. Then, relation R is said to be reflexive; if…

Q: Determine whether the relation R on A is an equivalence relation and provide your reasoning: а.…

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Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

Q: x R y in R if x- y < 3 |

A: Note that for any real number x, |x-x|=0&lt;3.  Thus, xRx or the given relation is reflexive.

Q: Check whether the following relations are reflexive, symmetric, transitive and anti-symmetric and…

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Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

Q: Let A = {1, 2, 3, 4, 5} and R be the relation defined by R = {(1,1), (2,2), (2,4), (2,5),…

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Q: Subject: Set Theory

A: • Transitive relation means that, whenever an element a is related to an element b and b is related…

Q: Write down all of the properties that each of the following binary relations satisfies from among…

A: The objective is: (a) To write down all the properties for “has a common language with” relation on…

Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: To find an equivalence class of x ϵ X determined by the relation R ⊆ X ⨯ X, R must be an equivalence…

A: Equivalence Relation: A relation R in X is called an equivalence relation if it is reflexive,…

Q: Check the following relation R on the set A = {1, 2, 3, 4]} is reflexive, symmetric and or…

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Q: b. Let us consider the sets A = {2,3,4,5} and B = { 0,1,2,3}. Define the relation R: A → B such that…

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Q: Which of these relations on the set of all people are equivalence relations? Determine the…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: Define: what is an equivalence relation?

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Q: State the formal definitions that a relation must satisfy in order to count as Reflexive, Symmetric,…

A: Reflexive relation: A relation R is reflexive over element X if every element X is related to…

Q: 9.42. Prove or disprove: The union of two equivalence relations a nonempty set is an equivalence…

A: We are asked to prove or disprove, the union of two equivalence relation on a non empty set is an…

Q: Define a relation ~ on the set of real numbers by X~ y means | x |+|y|=|x+y|. Determine whether - is…

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Q: a) If R and S be two relations from set A to B. Show that (RNS)-¹ = R-¹ S-¹ b) Justify the following…

A: We know that ,  A relation R defined on a set A is called equivalence relation if R satisfies the…

Q: Let R C R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given, R⊆ℝ+×ℝ+ with               R= x, y | x=y

Q: b) Write out, using set notation, the equivalence class for the point (0, 2)

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Q: (b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations…

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Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: Not reflexive.  Symmetric.  Transitive.  Not Equivalence relation.

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,

Q: 9.16. Let A = {a, b, c, d}. How many relations defined on A are reflexive, symmetric and transitive…

A: given A=a,b,c,d claim- how many realations defined on A are reflexive , symmetric and transitive and…