Algebra : Linear Quadratic Equations - Practice Questions

May 28th, 2015
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1. The question for the day is a sample practice problem in quadratic equation. Helps understand concepts related to roots of a quadratic equation and the nature of the roots of the quadratic equation.

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ABSTRACT ALGEBRAEQUIVALENCE RELATIONBy:Asri Damayanti3115106660SBI Class of Mathematics Education 2010STATE UNIVERSITY OF JAKARTA2012Abstract Algebras Replacing CourseMeeting: 10 Day, Date: Thursday, May 3rd, 2012Reason: because i got fever EQUIVALENCE RELATIONExample:G be any group. For we declare that if there exists an such that . We claim that this defines an equivalence relation on G.Proof:ReflexivityWe want to prove ,Then, can be , so is trueSymmetryWe want to prove that Then, from we got , from we got , since, and is true, therefore is trueTransitivityWe want to prove that Then, from we got , from we got , elimination then or . Therefore, . So, is true Thus, . We shall denote in this case as and it called the conjugacy class of in G.Proof:Since, , we have .We want to show that, if:a. , orb. a. Suppose that , let and We get, and c is not equivalence relation of bBy symmetric properties of equivalence relation, then By transitivity properties of equivalence relation, we get a is not equivalence relation of bTherefore, b. Suppose that , let then, by the definition of class since , and since Therefore, Because then by symmetric of equivalence relation it can be ,And so, since we have by transitivity of equivalence relationThus, , let , then Since, , then we get , hence Thus, and the argument is obviously symmetric in a and b, so we h

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