1) Define a relation on the set of all people as follows: two persons x and y are related if and only if both have last names that starts with the same Latin letter (for example, Peterson, Pauli, Punjab, Pokamun, Pokrowski, and so on…). Determine if this relation is Reflexive, Symmetric, and Transitive. Explain why or why not.

Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

Q: 2. For each of the following relations, indicate whether it is a partial order, a strict order, or…

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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: On the set A = {a, b, c, d, e, f, g, h} is given by the relation R = {(a; b), (a; c), (a; d), (a;…

A: The set is A=a, b, c, d, e, f, g, h and the relation is R=a; b, a; c, a; d, a; e, b; f, c; f, d; g,…

Q: Let A = {1, 2, 3}. Then show that the number of relations containing (1, 2)and (2, 3) which are…

A: The smallest reflexive relation on set A containing (1, 2) and (2, 3) is

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: Is the relation of “mapping” between two sets used to determine cardinality - and not used to…

A: Note- Since you have asked multiple question, we will solve the first question for you. If you want…

Q: Consider the following relation on set B = {a, b, {a}, {b}, {a, b}}: P = {(a, b), (b, {a, b}), ({a,…

A: Given that, The set B is: B=a, b, a, b, a, b And, the set P is: P=a, b, b, a, b, a, b, a, b, a, a, a

Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

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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: 4. Suppose R is a relation on a set A. The complementary relation R is defined by letting a R b if a…

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Q: In the set A = {1,2, 3, 4} is defined a relation R by ? = {(1,1), (1,3), (3, 4), (4, 3)}. ndicate…

A: Given A = {1, 2, 3, 4} R = {(1, 1), (1, 3), (3, 4), (4, 3)}

Q: If S is a relation from a non-empty set A to a nonempty set B then

A: Solution :-

Q: We defined the relation between sets by A ~ B means that there there is a 1-1 correspondence ƒ : A →…

A: We define the relation ~ between sets by A~B means that there is a one-one correspondence f:A→B Show…

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. draw a…

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

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Q: Show which of each of the three properties "reflexive, symmetric, and transitive" apply to each of…

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Q: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

A: Given a set A={1,2,3,…,15} define a relation induced by a partition of set A and that partition must…

Q: let A be the relation on the set integers defined by s A t if and only if |a| <= |t|  is the…

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

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Q: Which of the following relations is the Symmetric relation over the set A= {3,5,13}…

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Q: 1. Let & be the relation of (a,b) la #b] on the set of integers. What is the reflexive closure of R?

A: As per our company guideline we are supposed to answer only one question with its 3 subparts. Here…

Q: Without using the ?∞i=1 Ri representation of R+, Prove that for any set relation R (we did not pick…

A: Given: Let us consider the given, R+=∩Q:R⊆Q∧Q is transitive and prove that for any set relation R.

Q: Construct the Hasse diagram for the subset relation on the set P({a,b,c}).

A: Hasse diagram for subset of given set is made below

Q: A relation that assigns to each element x from a set of inputs, or ________, exactly one element y…

A: To fill: The blanks of statement: Given: The statement is "A relation that assigns to each element x…

Q: Determine for the following relations on the set of people if the relation is an equiv- alence…

A: We have 4 relations in our hand. We need to decide whether they are An equivalence relation A…

Q: 9.4. Let A = {a, b, c} and B = {1,2,3,4}. Then R1 = {(a, 2) , (a, 3) , (b, 1),(b,3), (c, 4)} is a…

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Q: Given R = {(m, m), (s, s), (e, e), (m, e), (s, e), (s, m), (e, m)} is a relation on set A = {m, e,…

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Q: Suppose A is a set and R is a reflexive and transitive relation on A. Show that the

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Q: 7. Consider the following relations on the set A = {- -3, –5 – | R = {(-3, –3), (–3, –5), (-3, –7),…

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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: Consider the subset relation C on the power set of {a,b,c}, that is P{a,b,c}. (a) Construct the…

A: Let S be a partially ordered set. Use the following definitions, to obtain the solution. Let a,b∈S…

Q: Subject: Set Theory

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

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: Let R be the relation on set {a,b,c,d} containing ordered pairs (a,c),(b,b),(b,a)(c,a)(c,d) and…

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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: e) Suppose that S is an equivalence relation on a set A = {1,2,3, 4, 5, 6, 7}. If 4 e [3] n [5],…

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Q: 4. Prove that the next relation is equivalence relation on the set of all people: {(x, y)|x and y…

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Q: 1. Let A = {cat,dog,bird,rat} and R be a relation on A defined by {(x,y) : x and y have at least one…

A: We have to solve given problem:

Q: This question refers to unions and intersections of relations. Since relations are subsets of…

A: The given sets are: A={-2,2,3,5} and B={2,3}

Q: R = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6 e (yes or no) whether R has…

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Q: 1. Let A = {a, b, c} and B = {r,s, t, u}. Furthermore, let R = {(a, s), (a, t)}, (b, t) be a…

A: Suppose A and B are non empty sets. Define a relation R:A-&gt;B then, Domain of R={x: (x,y) belongs…

Q: How many relations are there on the set {a, b, c, d}

A: Introduction: The relation is a subset of the Cartesian product of two sets. Since it is a subset of…

Q: Let R be the following relation on the set of all people. R= {(a, b) : a and b share a common…

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Q: 1. Consider the following relations defined on the set {a, b, c}. For each relation, determine…

A: (a) Reflexive functions are the ones whose domain and range are the same  for instance a,a∈R1 So…

Q: (1) Let A-(a,b,c,d), define a relation R on set A as follows: R-((a,a). (a,b), (b,a), (b,b), (c,c),…

A: Reflexive relation:  A relation R on set X is said to be reflexive if for all elements x∈X we have…

Q: For each of the following relations on sets {a, b, c, d}, decide whether it is reflexive, symmetric,…

A: As per Bartleby guidelines i can answer only one question or its sub three parts kindly upload rest…

Q: Consider the following two statements: (1) If a relation on a nonempty set is reflexive, then it is…

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Q: If R = {(1,2),(2,1),(2,2),(3,4)} is a relation on the set {1,2,3,4}.The reflexive closure of R is :

A: Given that R=1,2,2,1,2,2,3,4 is a relation on a set 1,2,3,4  Consider A=1,2,3,4