Show that if AB BA, then eA+BeAeB, but if they do commute, then the relations hold

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 = {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: ) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.

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Q: Given a natural number c ∈ N. On natural numbers, the relation Rc is defined as follows: ∀ a, b ∈ N…

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

Q: Prove that the relation of congruence is an equivalence relation.

A: A relation is said to be an equivalence relation if and only if the relation is reflexive, symmetric…

Q: Given a relation, R on A = {a, b, c, d} on as follows: R = {(а, а), (а, b), (а, d), (b, b), (b, с),…

A: Relation as a Matrix: Let A = {a1,a2,a3,.......am} and B = {b1,b2,b3......bn} are two finite sets,…

Q: 2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is…

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Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

Q: Disprove that for any relations R and S, ran(S • R) = ran(S).

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

A: Given: A = {1, 2, 3}

Q: Give an example of two equivalence relations R and S on

A: Consider that R and S are equivalence relations on A=1, 2, 3.

Q: Let Asfl,2,3} and The relations Ri=f(),(2,),(3,2) | find the following Ye lations

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Q: Use the Ruler axiom to prove that there is a one-to-one correspondence between any two lines.

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Q: Suppose R and S are relations on {a, b, c, d}, where R = {(a, b), (a, d), (b, c), (c, c), (d, a)}…

A: we have given relations R and S on {a, b, c, d} and we need to find composition R∘S

Q: Determine whether the following statements are True or False: - Part A: Suppose R1 and R2 are…

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Q: Given a natural number c ∈ N. The relation Rc is defined as follows: ∀ a, b ∈ N :  (a, b) ∈ Rc ⇔ (∃…

A: According to Bartleby guidelines , i can give answer only first three subparts of your problem. I…

Q: Which of the following relations contain cach of the following pairs (1, 1), (1, 2), (3, 2), and…

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Q: Show every possible 1-1 correspondence between the following sets. {a, b, c} and {1, 2, 3}.

A: Possible 1-1 correspondence between two sets

Q: that P ◦ Q is an equivalence relation on X iff P ◦ Q = Q ◦ P

A: Concept:

Q: let R be the relation on the set A = {1, 2, 3, 4, 5, 6} defined by a R bif and only if a = 2b.

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Q: Draw a single Venn diagram that represents the relationsh

A: Introduction: A Venn diagram could be a graphic that employs circles to depict relationships between…

Q: 11. If |A| = 3, how many relations are there on A?

A: Given A=3

Q: If A and B are independent, prove that B and the complement of A are independent.

A: Given,A and B are independent events , so P(A∩B)=P(A)×P(B) .

Q: Let R = { ( a,b ) | a,b ∈ Q and a − b ∈ Z } . Prove that R is an equivalence relation on Q

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Q: Given the following relations on the set {1, 2, 3} and R = {(1, 1), (1, 2), (2, 1), (1,3)}. Which of…

A: Given problem:- Given the following relations on the set {1, 2, 3} and R = {(1, 1), (1, 2), (2, 1),…

Q: Given a natural number c ∈ N. The relation Rc is defined as follows: ∀ a, b ∈ N :  (a, b) ∈ Rc ⇔ (∃…

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Q: Let Let A={2,4} and B = {1,3,5} and define relations U, V, and W from A to B as follows. For all (x,…

A: Given that -  Let A={2,4} and B = {1,3,5}

Q: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b) : |a –…

A: Given: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b)…

Q: a) Let A = {4, {$}, ($, [$}}} and B = {1,2}. How many equivalence relations on A?

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Q: If R, T, G,H are relation on A and RET,GCH then, 1. RoG CTOH 2. Тон с RoG 3. RoT S Goн 4. RoH E ToG…

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Q: Show that if for a relation R we know that R2 C R, then R transitive, and conversely. Ent. There are…

A: To prove whether a relation is transitive or not

Q: 9.15. A relation R is defined on Z by a Rbif |a – b| < 2. Which of the properties reflexive,…

A: Given : A relation is R is defined on Z is given by  a R b if a-b≤2  Which of the properties…

Q: Which of these relations on {0, 1, 2, 3} are equivalence ?relations

A: Equivalence relations are the relations which are reflexive (xRx), symmetric (xRy implies yRx),…

Q: Select the following relations on Z that are equivalence relations. ○{(a,b) ||a| = |b|} {(a,b) a²b²…

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Q: Obtain the 16 relations of the set {0,1}, indicate which of these are reflexive, symmetric and / or…

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Q: 1) Either prove or disprove the following statements: i) transitive. If binary relations T and S are…

A: Given: T and S are transitive  Suppose a,b∈T∩S, b,c∈T∩S ⇒a,b∈T, b,c∈T Now as T is transitive . So,…

Q: a) If R and S be two relations from set A to B. Show that (RNS)-¹ = R-¹ S-¹ b) Justify the following…

A: We know that ,  A relation R defined on a set A is called equivalence relation if R satisfies the…

Q: Let A = Z. Define R to be the relation where a~b if ab > 0. Then R is equivalence relation.

A: We have given the set A = { Z : the set of integers }  R= { (a,b) : a,b belongs to Z and a.b &gt;0}…

Q: Give examples of relations R and S on Z such that  Both R and S are not equivalence relations but R…

A: We need to find two set which are on equivalence on Z but their sum do.  LEet, R= a&lt;b S=a&gt;b…

Q: For all relations R and S, Ro S = So R. O True O False

A: Ans : False

Q: Determine which of the folowing relations R on Z are oquivaknee relatinns. If R is not an equivakner…

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Q: Our universe U is Z (integers), and R is the relation defined by R(x,y):=x<y^2 For example,  R(3,-2)…

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Q: For universe S = R², define relation ~= as: (a,b) ~= (c,d) < 2a - b = 2c - d Prove that ~= is an…

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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: (b) Let R and S be two equivalence relations on X. Are RnS, RUS, R \ S, also equivalence relations…

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

A: A={-4,4,7,9}B={4,7} A×B=-4,4,-4,7,4,4,4,7,7,4,7,7,7,4,7,7,9,4,9,7

Q: Prove or disprove: 1. For any relations R and S, ran(S • R) = ran(S). 2. If R and S are equivalence…

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Q: Let R and S be reflexive relations over set A. Prove or disprove that RnS is reflexive

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