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In Z, let . Prove that Z = HK. Does Z = H × K

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian ISBN: 9781133599708 52

Solution for problem 34E Chapter 9

Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

Contemporary Abstract Algebra | 8th Edition

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Problem 34E

Problem 34E

In Z, let . Prove that Z = HK. Does Z = H × K?

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Test 3 Study Guide  Determinism­ theory that the future is fixed by the past, there is only one possible future  Indeterminism­ the future is not set by the past, past has only limited effect on the future & future is not yet determined  Compatibilism (soft determinism)­ freedom and determinism can coexist, we can have free will even if there is only one future; ability to act on different hypothetically possible desires is all that is required for freedom  Traditional compatibilism­ we are free provided that we are acting on our will and are not constrained  Deep self compatibilism­ our will is genuinely free only if we act on desires we have chosen and that we identify with  Incompatibilism­ free will can only exist is determinism is false  Fatalism­ some events in the future cannot be avoided no matter what we do (most fatalist are not determinists, but it is possible to combine the two)  Libertarianism­ the future is not determined by the past. Future is open and we have the power to shape it. (these powers allows agents to have free will)  Hard determinism­ we have no free will because determinism is true, free will is an illusion and the past decides the future  Consequence argument­ argument for incompatibilism that claims that determinism is not compatible with moral responsibility (We are not responsible for our future actions)  Event causation­ the process of one event causing another  Agent causation­ an agent can act without prior events necessitating the agent’s action, agent can act spontaneously to cause something to happen  Thinking about the problem of free will has alerted us to the need to look at our own being more closely than we normally do day­to­day  Agency theory­ event causation happens regardless, we as agents insert ourselves into this timeline to change course of action  Principle of sufficient reason­ everything must have a reason or a cause  Free will is illusion because you have to make the choices you make. External forces cause decisions.  Basic argument (Strawson) – we are not responsible for past & laws of nature  we are not responsible for developing our character  we are not responsible for decisions we make.  Libet & Wegner (neurologists) believe events that occur in brain to make decisions are cause of our actions & feeling of consciousness  reactions in brain lead us to make choices.  Thinking about the problem of free will alerts us to look at our own being more closely.  The existence of free will relates to if we are responsible for actions or not.

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Chapter 9, Problem 34E is Solved
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Textbook: Contemporary Abstract Algebra
Edition: 8
Author: Joseph Gallian
ISBN: 9781133599708

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In Z, let . Prove that Z = HK. Does Z = H × K