Let the relation R on the set of ordered pairs of positive integers be defined as (a, b) R (c, d) a, b, c, d are positive numbers. Show that R is an equivalence relation. a + d = b + c, where

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Q: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b): a is a…

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Q: 4. Let R be the relation in the positive integers

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Q: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

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Q: Describe the equivalence classes of the relation R = {(a, b) : a € Z, b E Z, 13 divides (a – b)}

A: a equivalence class is a subset of the set on which the relation R is defined such that all elements…

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

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Q: 1. Let & be the relation of (a,b) la #b] on the set of integers. What is the reflexive closure of R?

A: As per our company guideline we are supposed to answer only one question with its 3 subparts. Here…

Q: Let S be the set of all real numbers and let R be a relation in S, defined by R = {(a, b) : a < b³}.…

A: Given relation is R = {(a, b) : a ≤ b3}

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

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

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Q: Determine whether or not the relation R on the set of all people is reflexive, symmetric,…

A: We will find whether the relation is reflexive, symmetric or transitive as following.

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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, b, c, d) and define a relation R on A as follows: R = ((a, a), (b, b), (a, b), (c, c), (b, a),…

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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.

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

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Q: Q1. Let A be a set of nonzero integers and let be the relation on A defined by (a, b) - (c, d)…

A: Solution:-

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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…

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Q: Let R be an equivalence relation on A. Find the maximum number of classes R can make if JA| = 80 and…

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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.

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

A: A ={ (a,b) : where a and b are positive integers}  R= {(a,b) and (c,d) : a+d= b+c }  We have to…

Q: 2. Let R be the relation on Z→Z such that ((a,b),(c,d)) = R a+d =b+c. Show that R is an equivalence…

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Q: 8. Let A be a set of nonzero integers and let R be a relation on A × A defined by (a, b)R(c, d)…

A: Equivalence relation