哲学逻辑代写 PHIL 1012代写 Introductory Logic代写 逻辑代写

PHIL 1012 Introductory Logic

Final Assessment

哲学逻辑代写 Instructions: Read these instructions carefully before beginning this assessment if you have not done so already. You must submit your answers

Instructions:

Read these instructions carefully before beginning this assessment if you have not done so already.

You must submit your answers as a single file upload. This file must be a PDF file. You can resubmit your answers as many times as you wish until the assessment closes.

You have several options for completing the assessment:

1. You may print this PDF and handwrite your answers in the space provided, before scanning and uploading your answers to Canvas.

2. You may directly annotate this PDF using a standard PDF annotation tool before uploading your answers to Canvas. (Make sure your annotations appear in the preview before and after submitting). 哲学逻辑代写

3. You may simply handwrite your answers on paper before scanning and uploading your answers to Canvas. If so, you must clearly label your answers. You do not need to include the questions.

4. You may use a word processor to write your answers before exporting to PDF and uploading your answers to Canvas. If so, you must clearly label your answers. You do not need to include the questions.

Answer all parts of all questions. The marks value of each question is shown below. The assessment as a whole is worth 50% of your final mark for the unit.

Clearly label your answers in your submission. Make sure that it is always clear exactly which question you are answering at any given point.

The assessment is partial open book: you may consult the textbook (Logic: The Laws of Truth), your course notes, lecture handouts, etc. You may not, however, consult general online resources.

It is a breach of academic honesty standards to share this document. It is forbidden to collude with other students, to share answers, and to seek or use shared answers. Evidence of misconduct in this regard will be taken very seriously.

Collusion or illegitimate cooperation is a form of academic dishonesty.

According to the University: 哲学逻辑代写

Cooperation is not legitimate (or appropriate) if it unfairly advantages a student or group of students over others. It can include working with a friend or group of friends to write an essay or report that is meant to be an individual piece of work. It can also include sharing quiz or test questions and answers with other students, as well as written assignments like reports and essays.

Penalties for academic dishonesty include a reduced mark for your work, or even failure in the unit of study.

I will be unable to respond to emails that do not concern technical issues relating to submitting the assessment during the assessment. If you are reading this before the assessment, now is the time to contact me with any questions about the content of the assessment. If you think there is a mistake in a question, do your best to answer the question as you understand it and provide an explanation of what you think the mistake might be. If there is a mistake in a question which means that it cannot be correctly answered then that question will not count towards your final grade.

1. [10 questions, 25 marks, 2.5 marks per part] 哲学逻辑代写

Translate the following into GPLI. Provide a glossary for your translations (either a running glossary for all of your answers, or a glossary for each answer). If you are unsure about your translation—for instance, if you think that there are multiple ways of interpreting the sentence—then provide a short justification of your choice of translation.

(i) Anne and Bobby are running and jumping only if Carla and Danny are too

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(ii) Anne introduced everyone who hadn’t already met Bobby to Bobby

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(iii) If only Bobby loves Anne then Bobby loves Anne but nobody other than Bobby loves Anne

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(iv) If someone cheats on their final assessment, they will face serious consequences

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(v) Every man loves some woman who doesn’t love him back

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(vi) Everyone—except Anne, Bobby, and Carla—is loved by Danny

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(vii) Someone other than Anne loves everyone who loves someone other than Bobby

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(viii) Exactly one boy loves Anne and that boy is Danny

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(ix) At least two boys love everyone except Anne

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(x) Nothing identical to itself is not identical to something not identical to itself

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2. [10 questions, 25 marks, 2.5 marks per part] 哲学逻辑代写

The following questions concern GPLI models. In each case you are asked to explain your answer. For the purpose of this assessment, you are expected to provide full and explicit explanations of your answers, making reference to the semantics of GPLI. We expect you to use the correct vocabulary in explaining your answers.

(i)

Is the following proposition true or false in the given model? Explain your answer.

i. ∀x¬(¬Cb ∧ Cx)

Domain: {1,2}

Referents: b:1

Extensions: C: {1}

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(ii)

Is the following proposition true or false in the given model? Explain your answer.

i. ∀z(Lcz ∧ Kbz)

Domain: {1,2,3,4}

Referents: c:1, b:2

Extensions: L:{⟨1,2⟩,⟨1,4⟩,⟨3,1⟩,⟨3,2⟩,⟨1,1⟩}, K: {⟨1,1⟩,⟨1,2⟩,⟨1,3⟩,⟨2,1⟩,⟨3,2⟩}

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(iii)

Is the following proposition true or false in the given model? Explain your answer.

i. (∀zCz → ¬∃xCx)

Domain: {1,2}

Extensions: C: {1}

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(iv)

Is the following proposition true or false in the given model? Explain your answer.

i. ∃z(Lbz ↔ ∀yLzy)

Domain: {1,2,3}

Referents: b:3

Extensions: L: {⟨1,3⟩,⟨2,1⟩,⟨3,2⟩,⟨3,3⟩}

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(v) 哲学逻辑代写

Is the following proposition true or false in the given model? Explain your answer.

i. ∀z(Kzz → (Kcz → Kzc))

Domain: {1,2,3}

Referents: c:2

Extensions: K: {⟨1,3⟩,⟨2,1⟩,⟨2,2⟩,⟨2,3⟩,⟨3,1⟩}

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(vi)

Provide a model on which the following proposition is true. Explain why the proposition is true on the model you have provided.

i. (Aa ↔ ∃yCy)

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(vii)

Provide a model on which the following proposition is true. Explain why the proposition is true on the model you have provided.

i. ((Lbb ∧ Jab) ↔ ∀xLxb)

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(viii)

Provide a model on which the following proposition is true. Explain why the proposition is true on the model you have provided.

i. ¬∀z∃xLxz

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(ix)

Provide a model on which the following proposition is true. Explain why the proposition is true on the model you have provided.

i. ∃x∃y∃z(Axyz ∧ x ≠ y ∧ x ≠ z ∧ y = z)

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(x)

Explain why there is no model on which the following proposition is true.

i. ∀x((Kxx ∨ ¬Kxx) ∧ x ≠ x)

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3. [5 questions, 25 marks, 5 marks per part] 哲学逻辑代写

The following questions concern GPLI trees. For each question, clearly state (i) your answer to the question and (ii) explain why the tree justifies the answer you have provided. Read each question carefully.

(i) Use a tree to test whether the following proposition is a tautology. If it is not, then, for every open path, read off a model on which the proposition is false. You must complete your tree. Briefly explain why the tree justifies your answer.

i. ∀x(a ≠ x ↔ (¬F xa ∨ F ax))

(ii) Use a tree to test whether the following propositions are equivalent. If they are not, then, for every open path, read off a model on which the propositions have different truth values. You must complete your tree. Briefly explain why the tree justifies your answer.

i. ∀x(F x → Gx), ∀x¬(F x ∧ ¬Gx)

(iii) Use a tree or a pair of trees to test whether the following propositions are contraries, contradictories, or neither. You must complete your tree or trees. Briefly explain why the tree or trees justify your answer.

i. ¬(∀xF x ∨ ∃xGx), ¬(¬∀xF x ∧ ¬∃xGx)

(iv) Use a tree to test whether the following argument is valid. If it is not, then, for every open path, read off a counter-model. You must complete your tree. Briefly explain why the tree justifies your answer.

i. ∀xx = c, (a = c → ∀xGxx) ∴ (b = a ∧ b = b)

(v) Use a tree to test whether the following argument is valid. If it is not, then, for every open path, read off a counter-model. You must complete your tree. Briefly explain why the tree justifies your answer.

i. ∀xx = c ∴ (a = c → ∀xGxx)

4. [5 questions, 25 marks, 5 marks per part] 哲学逻辑代写

The following questions require you to demonstrate a deep understanding of some of the central concepts from the unit. Read each question carefully. Answers up to 150 words will generally be sufficient to demonstrate deep understanding.

(i)

Convert the following proposition into an equivalent proposition using only the connectives ¬, ∧, and ∨, and the existential quantifier ∃ (e.g. ¬∃x¬(F x ∧ ¬Gx)). You do not have to use all of the connectives. Briefly explain/justify each step you have taken in making the conversion.

i. ((∀x¬F x ∨ ∀x¬Kx) → ∃x(F x ↔ Kx))

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(ii)

Consider the following truth table for the connective #:

What would the unnegated tree rule for the connective # have to look like, in order to have the property of ensuring that if all of the propositions on a path are jointly satisfiable before the rule is applied, for every path all the propositions on the path are jointly satisfiable after the rule is applied? Draw the tree rule and briefly explain your answer.

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(iii) 哲学逻辑代写

We know that if ∀xGx is true in a model then ∃xGx is true on that model. We also know that it is not the case that if ∀x(Gx → F x) is true on a model, then ∃x(Gx∧F x) is true on that model. Is there a class of models such that if ∀x(Gx → F x) is true on some model in that class, then then ∃x(Gx ∧ F x) is true on that model? If there is, what is that class of models? Explain your answer. (By ‘a class of models’ I mean something like this: ‘the class of models with at least two objects in the domain that assign the name ‘a’ the first object in the domain as its referent’).

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(iv)

Suppose that the premises of some valid argument in GPLI are logical truths—that is, they are true on every model. Does it follow that the conclusion of the argument is a logical truth? Explain your answer.

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(v)

We know that the following MPL proposition will generate an infinite tree: ∀x∃y(Gx ∧ Gy)

Construct the first part of the tree and then explain why this proposition generates an infinite tree. Is it possible to convert this proposition into an equivalent proposition which does not generate an infinite tree? If so, describe the equivalent proposition and briefly explain why (i) it is equivalent to the original proposition and (ii) it does not generate an infinite tree.

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