Let W be the set of words in the English language. Define a relation R on W by W₁ R W₂W₁ and we have a letter in common. Which properties of equivalence relations does R satisfy? (Select all that apply.) The relation is reflexive. The relation is symmetric. The relation is transitive. none of the above Explain.

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A: Any Relation is said to be equivalent if  it Reflexive , Symmetric and Transitive

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Q: Here is a diagram for a relation R on a set A. Write the sets A and R. 0 3 4 5

A: We have been given a diagram for a relation R on a set A. To Do: We have to write the sets A and R.

Q: Which of the following relations are transitive? The relations are in bold. (Remember: A relation R…

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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: Define a relation D on the set of real of numbers as follows: Vx, y ER, xD y ⇒x-y is rational…

A: Correct option is  D is reflexive , symmetric and transitive.

Q: 1. R is the relation defined on Z as follows: Vm, n € Z, mRn 5|(m² — n²). (a). Prove that R is an…

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Q: Define a relation D on the set of real of numbers as follows: Vx, y ER, x Dy ⇒ x-y is rational…

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Q: A relation R is defined on the set of integers by: aRb = a + b = 2m + 1, where m is an integer. Show…

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Q: If a relation is an equivalence relation, state the set of equivalence classes.

A: For the given relations To check the properties (i) Reflexive (ii) Symmetric (iii) Transitive.

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

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A: According to the given information it is required to check whether the given relation in each part…

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A: Definition of relation on a set X.

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A: A relation defined on set A is said to be an equivalence relation, if it is: 1) Reflexive relation…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by  R=1,1,2,2,3,31,2,2,1 And…

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A: Given that, a set   , then by the Cartesian product  will be the sell of all possible ordered pairs…

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A: Definitions of symmetric, reflexive,transitive are given.We have to check them .

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A: According to the guidelines,we can solve only first three subparts.