For universe S = R², define relation ~= as: (a,b) ~= (c,d) < 2a - b = 2c - d Prove that ~= is an equivalence relation on R², or find a counterexample.

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…

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Q: disprove: a relation that is symmetric and transitive must TProve also be reflexive. or

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A: Line L is parallel to itself. This means L is parallel to L.So, (L,L)∈RSo, R is reflexive.

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Q: The domain of relation R is ZxZ. (a, b) is related to (c, d) if a s c and b s d. Which statement…

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Q: а) The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5,…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

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

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Q: |Given the relation R= {(1,1), (2, 4), (3, 1), (4, 1), (5,2)} on the set A= {1,2,3,4,5), find the…

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A: Given, R1 and R2 are equivalence relations in a set A. So, both R1 and R2 are Reflexive, Symmetric…

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A: S=1,2,3,a,b,c To find: (a) , (b) , (c).

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Q: Let A- {#, 7, x} and let R be the relation on. A given by R {(7, 7). (#, #)}. Prove or disprove…

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Q: 1. Consider the relation R1: R2 - R such that (r1, y1)R1 (x2, y2) if and only if both points are on…

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Q: Define: what is an equivalence relation?

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Q: The relation R on A = {3, 5, 7, 9} is defined by the ordered pairs below: R= {(3, 3), (3, 9), (5,…

A: Reflexive Relation: A relation R on a set A is said to be reflexive if  (a,a)∈R   for every a∈A.…

Q: Is this relation

A: Using definition of relation

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Q: Let R be a relation from set A to B, if R is symmetric then its inverse will be...... Answer (Please…

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

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Q: Explain why consimilarity is an equivalence relation on M,.

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Q: We defined the relation between sets by A - B means that there there is a 1-1 correspondence f : A →…

A: The complete solutions is in given below

Q: What is equivalence relation

A: For a set A, a relation R defined on A is called EQUIVELENCE RELATION, if it is REFLEXIVE, SYMMETRIC…

Q: Determine whether the given relation is an equivalent relation on {1, 2, 3, 4, 5}. If the relation…

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