Problem 2 Let A be a set, and let R be a relation on A. Suppose that R is symmetric and transitive. Find the flaw in the following alleged proof that this relation is necessarily reflexive. “Let x ∈A. Choose y ∈A such that xRy. By symmetry know that yRx, and then by transitivity we see that xRx. Hence R is reflexive.”

Q: If R is a relation defined from the Set A ={ 6,12,25,36} to the set B = {3,4,5,6} as follows: {(x,…

A: Part (i):   Relation set of R in the roster form:

Q: Given set B as B = {0,1,2,3,4}. Suppose set A is the relation and defined as a. A = {(x, y) E Z | xy…

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Q: Is the following statement true or false? If R is any symmetric relation on a set A, then R is…

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Q: please solve this abstract algebra question for me

A: (a) True

Q: 2. Let D be a relation defined on Z as follows: For all x, y € Z, x D y iffx|y. Determine if D is…

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Q: d. Ris a relation on Z* such that (x, y) e R if and only if there is a positive integer n such that…

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Q: Answer the following question accordingly:

A: Given set is  B={1,2,3,4}

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

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Q: 9. Let R+ denote the set of positive real numbers. Define a relation E on R+ as follows: a Eb if and…

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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: Let A = {3, 5, 7, 8} and define a relation S from A to A as follows: %3D For all (x, y) E A × A, (x,…

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Q: Let A = {3, 5, 7, 8} and define a relation S from A to A as follows: For all (x,y)∈A×A,(x,y) ∈ S if…

A: Solution : Given :             A = {3, 5, 7, 8} ,                         S is a relation from A to…

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: 4. Determine which properties (reflexive, irreflexive, symmetric, antisymmetric, transitive) does…

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Q: Which of the following is/are true for the relation R, where a is related to b (aRb), if and only if…

A: Suppose, A be any set and suppose R:A->A is a relation. Then, R is reflexive: if for every x in…

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: 1. Let R be the relation on N defined by "aRb if EN or 5| (b – a)". So for example (6,2) € R and…

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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: Define the relation R on set A as follows: xR y if and only if { x, y} C A or {x, y} c A, or {x,y} <…

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Q: 1. Let R be a relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by R = {(a, b) ∈ A × A | 4…

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Q: 1. Let R be the relation on N defined by "aRb if EN or 5| (b- a)". So for example (6, 2) € R and…

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Q: Show that if for a relation R we know that R2 C R, then R transitive, and conversely. Ent. There are…

A: To prove whether a relation is transitive or not

Q: q2-  91.2% of 1980 is: Select one: 18057.6 180576 180.576 1805.76 18.0576

A: We are asking to find 91.2% 0f 1980

Q: Draw the Hasse diagram for the relation C on the set P({1,2,3}).

A: According to the given information, it is required to draw the hasse diagram for the given relation.

Q: 9.13. Let S = {a, b, c}. Then R= {(a,b)} is a relation on S. Which of the properties reflexive,…

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Q: I have the following questions: " Let R = ∅ be the empty relation on a nonempty set A. Which of…

A: Recall  the fact that let  A be any set  and  .So, it is  a relation on This  relation is  called…