Let A= {1,2,3,4,5} and define a binary relation Ramong the subsets of A as follows: XRY XCY. a) Is R reflexive? Explain. b) Is R symmetric? Explain. c) Is R transitive? Explain.

Q: Fix a set X, and let S be a collection of equivalence relations on X. Is s U an equivalence relation…

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Q: Given a relation R on a set A, prove that if R is transitive, then so is R-1.

A: Suppose A be any set and R is relation defined on A. Then R is transitive if whenever (a,b)∈R and…

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: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked  multiple questions so as per guidelines we will solve  the first question for…

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: Let R be the equivalence relation on the set A ={ a, b, c, d } induced by the partition ( {a,b,c};…

A: Given A=a, b, c ,dpartitiona,b,c; d

Q: Let A = {a, b, c, d}. For each of the following relations of A, decide whether it is reflexive,…

A: We will answer the first 3 subparts since exact number of subparts is not specified. Please resubmit…

Q: Suppose that R is a reflexive and transitive relation on a set A. Define a new relation E on A by…

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Q: Let R be a binary relation R on Z, defined by: Vx, y € N*, x R y =3neN* such that y = x" (a) Show…

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Q: Let R be the relation on M = {1,2,3} with the following diagraph representation: Then O Ris…

A: using the definition of reflexive,symmetry and transitive , solution of the given problem is…

Q: Give an example of a relation on the set {a, b, c, d} which is symmetric and transitive, but not…

A: Any relation R from a set Ato A is reflexive if and only if for every x∈A , the pair (x,x)∈R Any…

Q: 4. Let A = {1,2,3,4). Find a non-empty relation on set A such that the given MI conditions are met,…

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Q: Prove the understated statements concerning the relation < on the set Z of all integers . If    x…

A: x = y  and     O < z

Q: A relationR on a set A is called equivalence if R is:

A: Equivalence Relation: A relation R on a set A is said to be an equivalence relation if and only if…

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 intergers such that (refer to image).

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Q: Let R be the relation on A × A , where A= {1,2,3,4} that is elements of this relation are pairs of…

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Q: Use a membership table to prove the following relation: * (An B) U (A n Bº) = A

A: We have to use membership table.

Q: Show that the relation R = ∅ on a nonempty set S is symmetric and transitive, but not reflexive

A: See the attachment.

Q: 1. Determine whether or not the relation R on the set of all people is reflexive, symmetric,…

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Q: Let D be the binary relation defined below. For all u, w e 2, u D w → w=u +7 or w= u - 7. Show…

A: Solution of given problem is as below: A binary relation is equivalance relation if it satisfies the…

Q: (b) Observe that all the relations in (a) are equivalence relations. Prove that this is true in…

A: Given: A is a nonempty set, and P is a partition of A. To show: The relation R is equivalence…

Q: Subject: Set Theory

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Q: For non empty binary relation R={(a, a).(a, b).(a, e).(b, b).(b, e).(c, C).(c, d).(d, d).(e, e)} on…

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Q: Prove the understated statements concerning the relation < on the set Z of all integers . If x…

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Q: 3. Given a relation R on a set A, prove that if R is transitive, then so is R-1.

A: We are given  that R is a transitive relation on a set A  Transitive Relation  A relation on a set X…

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

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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: Let R be the relation on the set of natural numbers given by the following rule: (n,m) ∈R if and…

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Q: Let RR be a binary relation on A={a,b,c}A={a,b,c} given by…

A: We check relationship is reflexive or not

Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b)} : a is…

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Q: Let R be the relation on the set of integers such that a R b if and only if a = b or a = - b.…

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Q: For non empty binary relation R={(a, a),(a, b),(b, a),(b, b),(c, c),(c, d),(d, c),(d, d)} on the set…

A: We have to solve given problem:

Q: Let A={(m,n)∣m,n∈N and gcd(m,n)=1} and define the relation ⪯ on A according to (a,b)⪯(c,d)⇔ad≤bc…

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Q: Let X be the set of all subsets of ℤ . Define a relation R on X as follows: Given two subsets of…

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Q: Let R be a relation defined on the set Z by aRb if floor value of a = floor value of b. What…

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Q: Use a particular counterexample to explain why R fails to be an equivalence relation is the…

A: We take counter example   9R10,10R11⇒9R  11

Q: 1 Let X be a nonempty set and let S be the collection of all subsets of X. Let R be a relation in S,…

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Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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Q: Sketch a digraph for a relation on the set {a, b, c, d} that is irreflexive and symmetricbut not…

A: Denote R by the relation on the set S={a, b, c, d} that is irreflexive, symmetric and not…

Q: . Determine whether or not each of the binary relations R defined on the given sets A are reflexive,…

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Q: Consider the set Z in which the relation R is defined by aRb if and only if a + 3b is divisible by…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Prove the understated statements concerning the relation < on the set Z of all integers . If x…

A: To prove: If x<y and y<z then x<z. Proof: The first inequality x<y suggest that the…

Q: Let A={(m,n)∣m,n∈N2 and gcd(m,n)=1}, and define the relation ⪯ on A according to (a,b)⪯(c,d)⇔ad≤bc.…

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Q: Determine which of the folowing relations R on Z are oquivaknee relatinns. If R is not an equivakner…

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Q: For non empty binary relation R={(a, a),(a, b),(a, e),(b, b),(b, e),(c, c),(c, d),(d, d).(e, e)} on…

A: According to the given information, it is required to check which of the following is true:

Q: Define a relation on the set {a, b, c, d} that is (a) irreflexive and transitive, but not symmetric.…

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Q: Determine whether the relation ? on the set of all people is reflexive, symmetric,  antisymmetric,…

A: We have to determine whether the relation R on the set defined in the parts (a) and (b), are…

Q: Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ER…

A: A ={ (a,b) : where a and b are positive integers}  R= {(a,b) and (c,d) : a+d= b+c }  We have to…

Q: Let 2 be a non-empty set. (a) Show that the inclusion relation in P (2) is an crder relation…

A: A partial order relation leads to poset which is very interesting.