Let S be the set of all binary strings. The relation R on S defined by aRb if a and b have the same length is an equivalence relation. What is the equivalence class [01]R of 01?

Q: Write an equivalence relation of Set A = {1,2,3,4,5,6}

A: Set A={1,2,3,4,5,6}

Q: In each item below, verify that ~ is an equivalence relation on the given set. Let S = Z × N. Define…

A: Since you have asked multiple questions, we will solve the Question Q (a) and (b) for you. If…

Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

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Q: How many equivalence relations on the set {1, 2, 3}?

A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

Q: {(a, b) acb, a and b are finite set of integers}

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Q: Let R = {(a, a),(a, b), (b, b),(a, c), (c, c)} be a partial order relation on Σ= {a,b,c}. Let ≤ be…

A: Given, is a partial order relation on . is the corresponding lexicographic order on , the set of all…

Q: 7. Let R be the following equivalence relation on the set A = {1,2,3,4,5,6};: R = {(1,1),(1,5),…

A: Equivalence class of R= R  =a=x∈A :aRx 1=1,52=2,3,63=2,3,64=45=1,56=2,3,6

Q: Show that the intersection of any collection of equivalence relations over a set A is also an…

A: We have to prove intersection of equivalence relations on a set is equivalence Let us suppose R and…

Q: Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b),…

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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: 2. Let R and S be equivalence relations. Prove that RnS is an equivalence relation.

A: Let A be a non-empty set. A relation R on A is said to be equivalence relation if it is reflexive…

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: Define a binary relation on the set S=(-3, -2, -1, 1, 2, 3} as follows: R= {(a,b) ab>0} %3D a. Find…

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Q: x R y in R if | x |=||

A: we have to find the relation R where R is defined by x R y in ℝ if x=y, equivalent or not.

Q: Give an example of an equivalence relation R on the set Q such that there are exactly three distinct…

A: We take the help of the signum function

Q: 2. Let R be a relation defined on the set of integers Z where a R b if a +b is even. Determine…

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Q: Let S be the set of real numbers. If a,be S, define a ~ b if a -b is an integer. Show that is an…

A: Let S be the set of real numbers. Given the relation R is define a~b if  a-b is an integer. To show…

Q: Show that the set T := {(x, y) E Z × Z | x+y is even number } is an equivalence relation on the set…

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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 L be a language. Let us define the relation R such that x Ry if for every string z we have that…

A: First to prove R is reflexive, For let consider x , then for every z  we have xz∈L↔xz∈L. Hence R is…

Q: Let A={1,2,3,4,5,6} and consider the following 3 subsets of A. A, = {1,3,5}; Az : %3D %3D %3D {2,4,…

A: Let A=1,2,3,4,5,6 and 3 subsets of A. A1=1,3,5; A2=2,4,6,A3=3,6 we have a relation xRy if and only…

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: Exactly one of the three relations below is an equivalence relation. For each of the three: State…

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Q: Let A be {a,b,c}. Let the relation R be AxA-{{b,a),(c,b)}. Which of the following statements about R…

A: In first question, first option is correct.