b) Let A = {2, 4, 6, 12, 16, 18, 24, 32} and R be the relation on A where x R y if and only if x | y. (i) Determine whether the relation R is a partial order on the set A. Justify your answer. (ii) Draw the Hasse diagram of the relation R on A, or explain whv the Hasse diagram does not exist.

Q: Let A = {0,1,2,3} and R be the relation on A given by R =…

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Q: 2. Consider the relation on A = {(1,0), (-1,0), (1,3), (2, 4), (-4,-8), (3,9), (3,6)}, defined by:…

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Q: Determine whether the given relations are partial order or equivalence relation on A = {1, 2, 3, 4,…

A: 1. This relation satisfies all the conditions of equivalence relation i.e reflexive, symmetric and…

Q: {0, 1, 2, 3, 4, ...} and define the relation - on A by: x~y if x – y is divisible by 3 Determine…

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

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Q: 1) Define a relation on the set of all people as follows: two persons x and y are related if and…

A: Reflexive: A relation is said to be reflexive, if (a, a) ∈ R, for every a ∈ A. Symmetric: A relation…

Q: Let A = {2, 4, 6, 12, 16, 18, 24, 32} and R be the relation on A where x R y if and only if x | y.…

A: A= 2,4,6,12,16,18,24,32 R is define as xRy if x/y  so, R = (2,2) (2,4), (2,6) (2,12) , (2,16) (2,18)…

Q: Let R be a relation on Z defined by (x,y)ER if and only if 5(x-y)=0. Formall state what it means for…

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Q: Let A = {1, 2, 3, 4}. Let R be the relation on A defined as follows:          R = {(1, 1), (1, 2),…

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Q: 1) Define a relation on the set of points in the coordinate plane by setting (x, y) <1 (x', y')…

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Q: 2. Let R₁ be a relation on the set A and R₂ be a relation on the set B. Let R be the relation…

A: A relation is a subset of Cartesian product of two sets. Therefore, every element in a relation set…

Q: Let R be a relation on the set A = {x € Z:1 < x < 100} defined as follows: x R y if and only if x-y…

A: Equivalence relation

Q: Let R be a relation on A = {1, 2, 3, 6} and R = {(1,6), (1, 1), (3, 3), (6, 1), (1,2), (2, 1), (2,…

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Q: Show that the relation R = ∅ on a nonempty set S is symmetric and transitive, but not reflexive

A: See the attachment.

Q: Let A = {1, 2, 3, 5, 6, 10, 15, 30} and R be a relation on A such that aRb if and only if a is a…

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Q: Let {2,3,4}{2,3,4} and {8,9,10}{8,9,10}. Define a relation H from A to B such that (x,y) ∈ H if and…

A: Given that:                      A={2,3,4}B={8,9,10}H is an relation from A to B such that: (x, y)∈H…

Q: Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all (x, y) ∈ A…

A: A=3,4,5B=1,2,3,4R=x,y: x∈A, y∈B ∋xy&gt;7 a. R=3,3, 3,4, 3,5, 4,2, 4,3, 4,5, 5,2, 5,3, 5,4, 5,5

Q: Let R be a relation on A = {2, 7, 8, 9} and R = {(8,8), (9, 9), (8, 2), (7, 7), (2, 2), (2,7)}. Are…

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Q: Let R be a relation over a set A = {a,b,c,d}. What kind of order is R?  Note: Select the order that…

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Q: 1) a. Let A = The set of numbers involve in your college ID. And R = {(x, y) | = 2 divdes (x³ + y}…

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Q: Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all…

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Q: 5. Let A=Z and R, ={(x,y):x-y is divisible by 5} be a relation on A . That is x R,y if and only if…

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Q: Let  A = {−5, −4, −3, −2, −1, 0, 1, 2, 3, 4}  and define a relation R on A as follows: For all x, y…

A: The set A is defined as: A = {-5, -4, -3, -2, -1, 0, 1, 2, 3 4} x R y ⇔ 3|(x − y). R is an…

Q: Give an example of a nonempty relation R on A = {1, 2, 3, 4} which is a. symmetric and transitive…

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Q: 1) a. Let A = The set of numbers involve in your college ID. And R = {(x, y) |→ 2 divdes (x³ + y} be…

A: College ID is 17F1722 a)So, by the given question,  A=the set of numbers involves in my college ID=…

Q: Let G = {−2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows. For every…

A: We know relation isna subset of cartesian product. Here V is subset of G*H where (x-y) /4 is an…

Q: Determine if the relation R = {(1,3), (1,4), (2,3), (2,4), (3,4)} is reflexive, symmetric,…

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Q: Let R be the relation on A × A, where A = {1,2,3,4}, that is, ele- ments of this relation are pairs…

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Q: Let Z be the set of integers and R be the relation on Z x Z defined by: (a.x)R(b.y) if and only if a…

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Q: A relation R is called atransitive if aRb and bRc implies cRa. Show that R is reflexive and…

A: Given a relation R is called atransitive if aRb and bRc⇒cRa Now shows in the following that R is…

Q: b) Let S = { (x, y) | x, y € R} and relation R on S defined by (x,y) R (p,q) if and only if x-p =…

A: We have S=x,yx,y∈R x,yRp,q  if and only if x-p=y-q   Reflexive property: A relation R is said to be…

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 diudes (x −…

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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…

A: If R is any symmetric relation on a set A, then R-1 is symmetric.Proof :1. Let R be any symmetric…

Q: b. Let us consider the sets A = {2,3,4,5} and B = { 0,1,2,3}. Define the relation R: A → B such that…

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Q: For the set A = {are, bot, cab, era)}, define the relation R on A to be: (x,y) eR if and only if…

A: As per the condition, in every order pair there should be only 1 letter in common.

Q: Let R be a relation on A = {5, 6, 8, 9} and R {(8,8), (5,5), (6, 8), (5, 9), (9, 9), (9,5), (6, 6)}.…

A: Given that  R=(8, 8), (5, 5), (6, 8), (5, 9), (9, 9), (9, 5), (6, 6)

Q: Q3. Let R be a relation on the set A = {1,2,3}, defined as follows: R = {(1,1), (1,2), (1,3), (2,…

A: We have to choose the correct option on the given relation.

Q: A relation on a set A is circular iff , y, z x~y and y~z implies z~x. Prove that a relation is an…

A: The relation on a set is a subset of the Cartesian product of the set. Therefore, each element is in…

Q: B. Let A = {1, 2, 3, 4}. Let R be the relation on A %3D defined as follows: R = {(1, 1), (1, 2), (1,…

A: Find if the given relation is reflexive, symmetric or antisymmetric.

Q: 7. Let A = {1,2,3,4}x{1,2,3,4}. Define an equivalence relation ~ by (x1,x2) ~ (x3,xa) iff xxx2 =…

A: Let A=1,2,3,4×1,2,3,4. The equivalence relation ~  is defined by,        "x1,x2~x3,x4 only if…

Q: 1. Let A = {0,1,2,3} and R a relation over A: R = {(0,0).(0,1).(0,3).(1,1),(1,0).(2,3).(3,3)} Check…

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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: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…

Q: Let R be a relation on {a, b, c, d}) defined as R = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c),…

A: Concept:

Q: Let R be a relation on A = {0, 3, 5, 8} and R = {(0,0), (5, 5), (3, 3), (5, 0), (8, 8), (8, 3), (0,…

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Q: 1. Let A = Z and R, = {(x,y):x² -y is even number} be a relation on A. That is xRy if and only if x²…

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Q: Let A be a nonempty set. Let ~ be a relation on ℘(A)defined by: Letting B and C be arbitrary…

A: Given: Let A be a non-empty set let~ be a relation on ℘(A) Let "A" be a non-empty set Let ~ be a…

Q: 6. Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A →B as follows: For all…

A: Answer for sub question a: Given A=9,11,12,14, B=1,2,3,4. The relation R:A→B is defined as follows:…

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