1. Verify that the relation ~ is an equivalence relation on the set S given. (a) S = R reals, a ~ b if a - b is rational. (b) S = C, the complex numbers, ab if |a| = |b|. (c) S = straight lines in the plane, a ~ b if a, b are parallel. (d) s = set of all people, a ~ b if they have the same color eyes.

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: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

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Q: (4) Pick another language and let the relation ♡ mean “this number written out in [your language]…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: 5. Identify each relation as linear, quadratic, or exponential. a) YA b) c) -4 -20 +2 -6 4 4 6 2 YA…

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Q: How can I prove that the relationship r^2 is a subset of r using the definition of composition?

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Q: Suppose the following relations are defined on the set of A = {-2, -1,0 1, 2, }, . List the pairs in…

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Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

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Q: If #: $ a,b,c} which of these celations are a funchion? Emplain, cab) CS

A: Solution : Given :    A= {a, b, c}  Set of relations are      a)    { (a, b), (b, c), (c, c) }…

Q: . The relation ⋆ means “this number written out in English has this many letters”. For example, 6 ⋆…

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Q: 9. The relation ~ defined on the set of natural numbers by a ~ b means 'a – b is even is : A. an…

A: Equivalence relation : A relation which is reflexive, symmetric and transitive is an equivalence…

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: 4. Let X be any finite set and define the relation R on P(X) by R= {(E,F)||E| = |F\, E, F € P(X)}.

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Q: Please show the following question in detail, I don't understand one bit of it, " Let R be a…

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Q: Define the relation ~ on the set R of real numbers by x~y if and only if x = -y. Show that ~ is not…

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Q: For each relation on {0, 1, 2, 3} below show that the relation is an equivalence relation, or show…

A: I have used the definition of equivalence relation

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Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

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Q: Which of these ordered pairs belongs to the "does not divide" relation on the set of positive…

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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…