(b) Define Equivalence Relation with an example. Give an example of a relation which is not symmetric but anti-symmetric. Give an example of a relation which is reflexive but not transitive.

Q: The relation on the real numbers R defined by a ~ b if both a > b and b>a is not an equivalence…

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Q: Let X be a set and an equivalence relation on X. Define : XX/ - by π(x) = [x]. Show that it is a…

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Q: If R; = { (a,b) asb},then this relation is: %3D Select one: O Reflexive, Symmetric, Transitive O…

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Q: The domain of the relation A is the set of all real numbers. zAy if (r-y| ≤2

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Q: Let A = {1, 2, 3, 4}. Give an example of a relation on A that is:    (a) reflexive and symmetric,…

A: Let A=1,2,3,4. To give an example of a relation on A that is:  (a) reflexive and symmetric, but not…

Q: A person’s birth date consists of the month, day, and year in which that person was born. The domain…

A: Here, relation R is given as a set of people where no two people in group can have same date of…

Q: Find the F.T. of the fall wing Signals (functions): F((t)=3 sgn(3t)- 1 1+jt W Ans: F(W)=— — 2πеw jw

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Q: Explain the following: Subject -- Discrete Structure 1. What is relation? 2. What is function? Give…

A: Solution 1: Relation:  Let A and B be two sets. A relation from A to B is a subset of A×B.…

Q: • Relation "z + y is divisible by 5" on integers z, y is an equivalence relation. Circle the answer:…

A: A relation R is called an equivalence relation if : R is Reflexive, i.e. aRa  R is Symmetric, i.e.,…

Q: The relation p = ((a, b) e R x R: 1+ ab > 0} is %3D (a) reflexive, symmetric but not transitive. (b)…

A: Given relation is ρ =  a, b ∈ ℝ × ℝ : 1 + ab > 0

Q: The domain for the relation R is Z × Z. (a,b) R (c,d) if and only if a <c and b< d. Indicate whether…

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Q: Determine whether the relation R is a partial order relation on the set of positive…

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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.

Q: Indicate whether the relation is: •Reflexive, anti-reflexive, or neither •Symmetric,…

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Q: The figure below shows an arrow diagram of a relation R. R d Is the relation reflexive? Select Is…

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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: The domain of the relation L is the set of all real numbers. For x, y e R, rLy if r < y.

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Q: Please help me with these questions. I am having trouble understanding what to do Thank you

A: Step 1 1) Definition of R1​ and R3​: R1​ = { (a, b) ∈ R2 ∣ a &gt; b }   (greater than relation)R3 =…

Q: 2. In the set of all US states, a relation is introduced such that aR b iff "a borders b". a. Is the…

A: Answer given below.

Q: How does number 1 differ than a relation? Please explain how, thank you. My teacher wants me to…

A: Relation: Let A and B be two non-empty sets. A relation R from A into B is a subset of A*B.…

Q: Let R₁ and R₂ both be equivalence relations. Show by proof or disprove by counterex- ample the…

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Q: Is this relation discrete or continuous? -50 -5 -5- O Discrete O Continuous

A: This relation is Discrete.

Q: Give an example of a relation which is (i) reflexive and transitive but not symmetric; (ii)…

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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…

Q: What is the domain of the graphed relation?

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Q: 3. Prove or disprove each of the following properties for the relation below: reflexive, symmetric,…

A: The given relation, which is defined on the set of integers, is…

Q: (c) The reversed relation R is an equivalence relation. (d) So R is an equivalence relation if and…

A: (c) If R is an equivalence relation in a set X, then it is reflexive, symmetric and transitive.

Q: What is a relation? What is Reflexivity What is Transitivity What is Symmetry

A: Relation:

Q: Define: what is an equivalence relation?

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Q: Tell whether the given relation is reflexive, symmetric, transitive on the set of all people.…

A: whether the given relation is reflexive, symmetric, transitive, equivalence.

Q: A partial order relation is that which is A Reflexive, symmetric and transitive B Reflexive and…

A: A (non-strict) partial order is a homogeneous binary relation ≤ over a set P satisfying particular…