Which of the following is not true? I. All relations are functions. II. Bijection is a function that is both injective and surjective. III. A relation on a set X is reflexive, if every vertex has a loop. IV. A relation R on a set A such that for all a,be A,if (a,b) e Rand (b.a) eR, then a=b is antisymmetric. O I and III O I and IV O l only IV only

Q: How many elements are in the Cartesian product U x V? * Let U = {u is odd | 9 < u < 14} and V = {v €…

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

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Q: Let W be the set of words in the English language. Define a relation R on W by W₁ R W₂W₁ and we have…

A: We are given that,      w1 R w2  &lt;=&gt; w1 and w2 have a letter in common.  Now, it is obvious…

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Q: If A (1,3.4) and R is a relation defined on A as: R = {(r.y) E Ax A:r-y is odd ), Then relation Ron…

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Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is:    (a) reflexive and symmetric,…

A: Let A=1,2,3,4. To give an example of a relation on A that is:  (a) reflexive and symmetric, but not…

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: Given a relation g from the set D = {1, 2, 3, 4, 5} to the set C = {a, b, c, d}, where g = {(1, a),…

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Q: Let A = {n| 3 < n S 30} and define a relation on A such that aRb iff a |b. List the relation set R.…

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Q: For each of the following relations, determine whether the relation is: Transitive. A partial order.…

A: Answer:Explanation:Reflexive: A relation on a set is reflexive if every element in the set is…

Q: A = Z*; a R b if and only if |a – b| < 2.

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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: 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: Part A: Suppose R is a relation defined on the set A = {1,2,3}. If R =…

A: Reflexive Property The Reflexive Property states that for every real number x , x=x . Symmetric…

Q: b) E Rif and only if a has the same first name as b. (Check all that apply.) Check All That Apply…

A: We need to check whether the given relation is reflexive, symmetric, transitive, antisymmetric. here…

Q: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: A relation R on a set A with elements a, b and c is said to be in a transitive relationship, then if…

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: Let A = {a, b, c, d} and define a relation R on A. The directed graph of the relation is shown here.…

A: We have: The relation is: R=a,c,b,a,c,d,d,b

Q: Which answer below best describes a relation on a set X? 0000 A relation is a A relation is a A…

A: Definition of relation on a set X.

Q: draw the graph of this relation. Search this relation

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Q: Ris a relation from A= {2,3,4} to A. The graph of the relation R is given by G = {(2,4), (4, 3), (3,…

A: Option A is correct.

Q: 6. Consider the set A = 10 = {0, 1, 2, ..., 9} and consider the relation R on A determined by a Rb…

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Q: Let R be a relation on Z given by aRb if and only if a = b². Is this relation a function? Justify…

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Q: Let X = {0, 1, 2, 3, 4}. Draw a relation R on X such that xRy if x + y = 4. a. Draw the graph…

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Q: Question 2 How many relations are there on the set A in Question 1? Give the reasoning for your…

A: As we know from the definition of relation on a set that every relation on a set is an element of…

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: Given a relation g from the set D = {1, 2, 3, 4} to the set C = {a, b, c, d} where g= {(1, a), (2,…

A: A relation  from the set  to the set  where .The objective is to determine whether the relation is a…

Q: C = {4x + 1] x € Z+}, D = {c + d]c € C, d € C}, E = C × D Is C a subset of D or E? Explain a…

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Q: Let A = {5, 6, 7, 8, 9, 10} Let R be a relation on A defined by R = {(a, b) : a e A, be A, Ja -…

A: Given,          Let A= 5,6,7,8,9,10  .           Let R be a relation on A defined by R=a,b :…

Q: 5. Let A = {6, 8, 10, 15, 17} and B = {2, 3, 4, 5} and define a relation R: A → B as follows: For…

A: Given: A={6, 8, 10, 15, 17} B={2, 3, 4, 5} Relation R:A→B is: For all x,y∈A×B∈R if and only if…

Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is (R = Reflexive, S = Symmetric, T =…

A: (a) Consider the Relation          V = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (2, 3), (3,…

Q: Given the relation R on the set of all integers defined by the rule (x, y) ER if and only if x 2 y².…

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