The relation D is defined on the set P = {6, 9, 15, 54, 78, 90} by the rule: n1 D n2 exactly if (n2 = (6 × n1)) ∨ (n1 = n2). (a) Draw a Hasse diagram for the relation D on P. (b)  State whether the relation D on P is an ordering or not. Explain your conclusions based upon the relation’s adjacency matrix, or other reasoning. (ii)  Let R = {(a, a),(a, b),(a, d),(b, a),(d, a),(d, b)} be a relation on the set {a, b, d}. (a)  Determine the adjacency matrix of R+, where R+ is the transitive closure of R. (b)  List the relation R+ as a set of ordered pairs.

Q: Given the set A- {a, b, c, d} a) If this is the relation R= {(a, b), (b, d)} Show s(R). b) If this…

A: Given R=a,b,b,d. The Symmetric closure of R denoted by sR=R∪R-1, where R-1 is the inverse of the…

Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b) , (a, c) , (b, c)} To obtain the…

A: Transitive relation means if (x, y) and (y, z) are in R, then (x, z) will also be in R.    Using…

Q: Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choosethe correct…

A: Given : Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}.  Choosethe…

Q: Define a relation R on N by m R n if and only if m #n. Explain why 8. this relation is or isn't…

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Q: Let A = {4, 5, 6} and B = {6, 7, 8} and let S be the "divides" relation from A to B. That is, for…

A: Here given sets A = {4, 5, 6} and B = {6, 7, 8} and relation defined asxSy⇒x/y means x, y∈S⇒x…

Q: Let R1 = {(a,b) E R²|a > b}, R2 = {(a, b) E R²|a < b} and a) R3 = {(a, b) E R²|a + b} be relations…

A: we have  R1={(a,b)∈R2|a≥b}R2={(a,b)∈R2|a&lt;b}R3={(a,b)∈R2|a≠b}

Q: Define the relation R = {(a.b): a + b < ab} = A x B with A = {1,2,4} and B = {2,5,6). List all the…

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Q: What is the range of the relation?

A: To finf the range of the relation.

Q: 4 1) 3 bes this digraph illustrate a relation that is symmetric or transitive or neither? ymmetrid…

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Q: 4. Let R be the relation {(1, 2), (1, 3), (2, 3), (2, 4), (3, 1)), and let S be the relation {(2,…

A: To find the composition of two relations R and S . the domain of S°R will be same as domain of R…

Q: Let Y be a relation defined by a Y b iff a times b is even. Is 5 Y 7 true?

A: Here, the given problem is on relation on set. We will solved the problem  step by step.

Q: 2 = y. Select the description that accurately describes The domain of a relation R is the set of…

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Q: What is the domain of the following relation? {(-4, -1), (-1, 2), (2, 3), (3, -5)} {-5, -1, 2, 3}…

A: The given relation is ,                          R=-4,-1 , -1,2, 2,3 ,3,-5 Recall :…

Q: Consider the relation A ≤ B if the properties of A are also contained in the properties of B. Let S…

A: Partial ordering :                     A relation R on a set A is called a partial order relation if…

Q: Let A = {a, b, c} Define a relation as follows: ARA = {(a, b), (a, c), (b, c)} To obtain the…

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Q: Decide whether each of the following relations is an equivalence relation or not.  {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Let A = {1, 3, 5, 7,9}, B = {2, 4, 6, 8}; a R b if and only if b< a a) Find Domain of the relation R…

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Q: For the relation, indicate whether the relation is: • Reflexive, anti-reflexive, or neither •…

A: A relation R defined on a set S is said to be Reflexive if xRx for all x in S.  Anti reflexive  if…

Q: Considering A as a set which contains the elements {2,3,4,5,6,7,8}, Define a relation R from A to A…

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Q: Let A = {4, 5, 10, 21, 24). List the ordered pairs in the relation R = {(a, b) E AXA: alb). (Recall…

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Q: By listing the elements as ordered pairs, define a relation on the set A = {e, 2, 7, ♡} which is:…

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

A: Relation R={(a,b)} is defined on set S={a,b,c}A relation R across a set S is reflexive if each…

Q: What is the relation between An B and AnB ? Justify your

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Q: Find the number of relations from the set A {a, b, c} to the set B = {1,3}

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Q: Consider the following relations R1, R2, R3, R4 on the set [4] = {1,2, 3, 4}. Each of the relations…

A: Here we use definition of function and relation

Q: 1. Consider the relation < on the set {1,2, 3, 4}. Write down this relation as a set of ordered…

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Q: What is the domain of the relation (8, 2), (6, 4), (4, 2), (2, 4)? O 2,4 O 2, 4, 6, 8 O 6, 8 O 2, 4,…

A: Concept: Domain is the set of all first elements of ordered pairs (x-coordinates).