1. Determine whether each of the following relations on the set {1, 2, 3, 4} is reflexive, symmetric, antisymmetric or transitive. (a) mi (2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4) } (b) (1, 1), (2, 2), (2, 1), (1, 2), (3, 3), (4, 4) } (c) (2, 4), (4, 2) }

Q: 2. For each of the following relations on the set {1,3,4, 7}. • R1 = {(7, 7), (1, 1), (4, 4), (3,…

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Q: Let B = {a, b, c}and S is the relation on B such that S3 (а, a), (а, b), (b, с), (а, с), (с, с).…

A: Given the set B={ a,b,c } and the relation S on B such that S={(a,a),(a,b),(b,c),(a,c),(c,c)}

Q: 1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m…

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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: 2. Define the sets X = {1,2,3} and Y = {4,5,6}. Now, define the relation R from X to Y by „R, if and…

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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: Theorem: If R is a fuzzy relation on the set X, then (R-1)-1 = R

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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: Consider the four following relations on A = {1,2, 3}: R = {(1, 1), (1,3), (2, 2), (3, 1)}, R2 =…

A: Relation

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

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Q: 14) For each of the following relations on the set {1, 2, 3, 4}, decide whether it is reflexive,…

A: The solution of the problem is given in the next steps.

Q: Consider the following relations on {1, 2, 3, 4}. R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)} R2 =…

A: “Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Consider the following relations on {1, 2, 3, 4}. R1 = {(2,2), (2,3),(2,4),(3,2),(3,3),(3,4)} R2 =…

A: This is a problem of relation.

Q: 12. Consider the following relations on {1, 2, 3, 4). R1 = {(2,2), (2,31.2,4).(3,2).(3,3).(3,4)} R2…

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Q: Let R be the relation on a set {1,2,3,4,5} containing ordered pairs (1,1),…

A: Given set is A = {1, 2, 3, 4, 5} and relation is R = {(1, 1), (1, 2), (2, 2), (2, 5), (3, 1), (3,…

Q: Let R, and R2 be relations on a set A = {1, 2, 3, 4}. In particular, let R, = {(1, 1), (1, 2), (2,…

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Q: ) 5. Determine whether the following relations are reflexive, symmetric, antisymmetric, and/or…

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Q: Let

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Q: Let A = {0,1,2} and r = {(0,0), (1,1), (2,2 y that r is an equivalence relation on A.

A: The relation is reflexive, since a,a∈R, where a∈A Also, since a=b where (a,b)∈R therefore, the…

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

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Q: Let R = { (1,1), (3,1), (2,1),(2,2), (1,3) } be a relation on the set A = {1,2,3}. Construct a…

A: The set A×A={(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)} R={(1,1), (3,1), (2,1),…

Q: Which of the following relations on the set {1,2.3,4} are reflexive, symmetric and transitive? R1 =…

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Q: 2. Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,2), (1,4), (2,1),…

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Q: 4.4.5 Write out the following relations as subsets of the Cartesian pod (a) The relation on N…

A: (a) The relation given is already a subset of the Cartesian product N x N. It can be written as…

Q: The following relation on the set {1, 2, 3, 4} that antisymmetric is... 1. OR = {(1, 1), (1, 3), (2,…

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

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Q: Given the following relation on set X= {1, 2, 3, 4, 5}: R= {(1,1), (1,2), (2,2), (2,3), (2,4),…

A: Consider the set X=1,2,3,4,5 R=1,1, (1,2), (2,3), (2,4), (3,1),(3,2),(3,3),(3,5),(4,4),(5,4),(5,5)

Q: 1. Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric,…

A: solution

Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

Q: 2. A. Consider the following relation on {1, 2, 3, 4, 5} R1 = {(1,1), (1,2)(2,1)(2,2), (3,4), (4,3),…

A: A=1,2,3,4,5A reflexive relation is the one in which every element maps to itself.Therefore reflexive…

Q: Question 6 For each of the relations on A ={1, 2, 3} below, {(1, 1), (1, 3), (3, 3)}, R = S = {(1,…

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Q: 1. Consider the following relations on the set A = {1,2, 3, 4}. = {(1, 1), (1,3), (1, 4), (2, 2),…

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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: 5. For each of the following relations, indicate whether the relation is reflexive, anti-reflexive,…

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Q: Let R be the relation on the set S = {1,2,3, a, b, c} given by xRy if and only if (а, у) € {(а, а),…

A: Given R be the relation on the set S=1,2,3,a,b,c given by…

Q: 12. Determine whether the following relations on Z are reflexive, symmetric, antisymmetric, and/or…

A: Nn

Q: Question 6 For each of the relations on A ={1, 2, 3} below, R= {(1, 1), (1, 3), (3, 3)}, S = {(1,…

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Q: B. By determining whether each relation on the set A = {1,2,3,4} possesses the types of relation in…

A: given set A=1,2,3,4 claim- by determining whether each relation on the set A possesses the types of…

Q: Which of these relations on {O, 1, 2, 3} are ?equivalence relations а) (0, 0), (1, 1), (2, 2), (3,…

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Q: Let R be the relation on the set {1, 2, 3, 4} containing the ordered pairs (1, 1), (1, 3), (1, 4),…

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Q: For each of these relations on the set {1,2,3,4}, draw the graph of the relation: {(1,1), (2,2),…

A: For each of these relations on the set {1,2,3,4}, to draw the graph of the relation.

Q: Let X = {a, b, c, d, e,f} and S be the relation on X defined by S = || {(а, а), (а, b), (а, с), (а,…

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Q: 3) Let A = {1, 2, 3, 4, 5, 6, 7, 8}. How many possible symmetric relations over A contain the…

A: Given A=1,2,3,4,5,6,7,8 contains the ordered pair 2,3,3,24,7,5,5 and 8,7 Since, for the diagonal…

Q: B. By determining whether each relation on the set A = {1,2,3,4} possesses the types of relation in…

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Q: 2. Consider the following relations on the set of integers: R1 = {(a, b) | a b}, R3 = {(a, b) | a =…

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Q: Find the transitive closure of the relation R={(1,2),(2,2), (2,3),(3,3)} on the set A=(1,2,3}.…

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Q: * ?Which of these relations on {0, 1, 2, 3} are equivalence relations a) {(0, 0), (1, 1), (2, 2),…

A: A and C are the equivalence relations

Q: For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is…

A: This is a problem of relation which is under discreet math

Q: 1. Consider the following relations and determine whether or not they are reflexive, symmetric, and…

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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: Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs {(0, 1), (1, 1), (1, 2),…

A: To find the transitive closure of a relation, we just add the ordered pairs that completes the…

Q: Which of the following relations is the a partial ordering on the set A = {3,7,9}? O…

A: A relation R on a set A is called a partial order relation if it satisfies the following three…

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…

Q: b) Let C = {1, 2, 3, 4}. Find a relation R on C that has exactly 3 ordered pair members and is both…

A: Given C = {1, 2, 3, 4}. We find a relation R on C that has exactly 3 ordered pair members and  both…