10.2.19 - x = y . Because equality is symmetric, we...

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INFS 501 10.2.19 Here x A y if and only if xAy x ∣=∣ y . This problem seems hard only because of the formalities using the definitions. Actually, reflexivity, symmetry, and transitivity follow simply from the fact that equality between numbers is reflexive, symmetric, and transitive. Is A Reflexive? Answer : Yes, A is reflexive because x ∈ℝ , x = x , so x A x. Is A Symmetric? Answer : Yes, A is symmtetic, here is why. Suppose x,y ∈ ℝ and x,y  ∈ A, so
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Unformatted text preview: x = y . Because equality is symmetric, we conclude y = x and y,x A, by the definition of A. Is A Transitive? Answer : Yes, A is transitive. Here is why. Suppose x,y,z , x,y A and y,z A. This means x = y and y = z . Thu s, x = y = z , so x = z , making x,z A by the definition of A....
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