reflexive, symmetric, antisymmetric, transitive they have. Write which of these is an equivalence relation.  3) Z is the set of integers, relation R:Z x Z is defined as a,b ∈ Z; aRb <=> | a - b | ≤ 2

Q: Let R be the relation on the set of integers, s.t., aRb if and only if a=b or a= -b. Is R an…

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Q: Let A be the set of all students of a boys school. Show that the relation Rin A given by R = {(a, b)…

A: It is given that, A is the set of all students of a boys school.Show that R is an empty…

Q: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: we have given a set  A = { 1, 2, 3, 4}  and R is a relation on the set A where R is defined as (a,…

Q: 4. Let R be a relation defined on the set of integers by a R b if a +b = 0 or a – b = 0. Determine…

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Q: Let R be the relation consisting of all pairs (x, y) such that x and y are strings of uppercase and…

A: Let R be a relation on a set A R is an equivalence relation if it is reflexive, symmetric,…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show  which…

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Q: Let R CR* x R† with R = {(x, y)|[x] terms of whether it is reflexive, irreflexive, symmetric,…

A: Consider the given information:

Q: What property is NOT included for an EQUIVALENCE RELATION? * O Reflexive O symmetric O Transitive O…

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Q: Which relation on the set {a, b, c, d} are equivalence relations and contain(i) (b, c) and (c, d)

A: The set {a, b, c, d}.

Q: n R m in Z if nm>0

A: 1) reflexive property : for all n in Z - {0}, we have, n R n because, n•n = n² &gt; 0 But, for n = 0…

Q: 10) Which of the following statements is false? a) fR is reflexive, then RnRep b) ROR' p R is…

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

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Q: Show which of each of the three properties "reflexive, symmetric, and transitive" apply to each of…

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Q: let A be the relation on the set integers defined by s A t if and only if |a| <= |t|  is the…

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

A: We are given the set A = {0, 1, 3, 5, 7, 8} and the relation R defined on A such that R = {(x, y)| 4…

Q: Prove that the following relations are equivalence relation: On Z× (Z−{0}), with (a,b)∼(c,d) if…

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Q: Let A = {1,2, 3,4,5,6,7,8,9} and R be a relation in A ×A, defined by (a, b) R(c, d) → a + d = b + c…

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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: Prove and say the name of the following equivalence relation x ~ y ⟺ x - y = 4k, k ∈ Z

A: x ~ y iff x - y = 4k , k in Z Implies that  x is congurent to y mod 4.

Q: 1. For (a, b) and (c, d) in R², define (a, b)R(c, d) by a² – c² = b2 - d². Determine whether the…

A: The given problem is to prove that the relation is equivalence relation, to be equivalence it must…

Q: Which relation on the set {a, b, c, d} are equivalence relations and contain (i) (b, c) and (c, d)…

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Q: Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b) : both a and b are…

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Q: Consider the relation R = {(a, b), (a, c), (c, b), (b, c)} on the set A = {a, b, c}. Is R reflexive,…

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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: Determine the following relation on the set {a, b, c, d}, is reflexive, irreflexive, symmetric,…

A: Let R represent a relation on a given set S=a,b,c,d. Then, relation R is said to be reflexive; if…

Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

Q: Consider the set Q = Z × (Z 10), and the relation fupon Q Defined as: (a, b) ↑ (c, d) + a•d = b•c a)…

A: we shall solve the part (a) only , if you want us to do other parts please resubmit the question…

Q: Define a relation on the set {a, b, c, d} that is 6. (a) irreflexive and transitive, but not…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Define a relation Q on the set Rx Ras follows. For all ardered pairs (w, x) and (y, z) in Rx R, (w,…

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Q: Check the following relation R on the set A = {1,2,3, 4} is reflexive, symmetric and or transitive…

A: Relation R on set A = {1, 2, 3, 4} and R is defined as, a,b ∈ R if and only if a≠b,∀a,b∈A.

Q: Let R be relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) e R…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Write down all of the properties that each of the following binary relations satisfies from among…

A: The objective is: (a) To write down all the properties for “has a common language with” relation on…

Q: Let R and S be any two equivalence relations on a non-empty set A. Then check whether ( R…

A: Introduction :

Q: Use a particular counterexample to explain why R fails to be an equivalence relation is the…

A: We take counter example   9R10,10R11⇒9R  11

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

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Q: Is the relation aRb → ab < 0 an equivalence relation on the set Z? Justify your answer.

A: Given a relation, aRb⇔ab≤0. To check whether R is an equivalence relation on set ℤ. A relation is an…

Q: Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a,…

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

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: 9.42. Prove or disprove: The union of two equivalence relations a nonempty set is an equivalence…

A: We are asked to prove or disprove, the union of two equivalence relation on a non empty set is an…

Q: Show that the relation R is an equivalence relation in the set A = { 1, 2, 3, 4, 5 } given by the…

A: Given- Set A={1,2,3,,4,5}. To Show- That the relation R is an equivalence relation in the set A = {…

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

A:

Q: Let R C R+ x R+ with R = {(x, y)|[x] = [y]}, that is, x and y round up to the sane number.…

A: Given, R⊆ℝ+×ℝ+ with               R= x, y | x=y

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: Check the following relation R on the set A = {1,2, 3, 4} is reflexive, symmetric and or transitive…

A: Not reflexive.  Symmetric.  Transitive.  Not Equivalence relation.

Q: Let S be a nonempty set. Consider the relation ~ on P(S) defined byA ~ B if A U BC = S. Is the…

A: Let S be a nonempty set. Consider the relation ~ on P(S)  defined by A~B if A∪Bc=S To show: "~" is…

Q: Either show the following relations on {0, 1, 2, 3} is an equivalence relation, or show which…

A: Either show the following relations on {0, 1, 2, 3} is an equivalence relation,