代做LINC12 Fall 2024 Monthly Assignment 2代写Processing

日期：2025-02-11 05:09

Monthly Assignment 2

LINC12 Fall 2024

October 25, 2024

Assignment due: Sunday November 3, 23:59 on Quercus

Total points: 45

The following exercises must be completed by uploading a PDF document onto Quercus.  This assign- ment covers material through the Thursday, October 17 lecture.

This assignment is worth 45 points altogether. It contains a variety of questions ranging from simple to difficult. It also includes problems that were presented as practice exercises. Refer to your notes from lecture for information on how to complete those problems.

If you work with anyone else, or discuss answers with your classmates, please indicate their names some- where on your returned answer document.  This is so we know to expect similar answers.  However, you should hand in your own unique work!

1            Predicate Logic (5 pts)

Translate the following sentences into Predicate logic.  You do not need to provide a model or a legend for constants in this question.

(1)    Robert likes Pia and Georgina.

(2)    Dr. Tannhaus resigned or disappeared.

(3)    Pilar gave Beng Beng to Qin Xue

(4)    Gregor is sick and asleep.

(5)    If Dr. Tannhaus resigned, Bronwyn will be happy.

2           Set Theory (6 pts)

Recall De Morgan’s laws from our work in Propositional Logic:

(¬p ∨ ¬q) ↔ ¬(p Λ q)

(¬p Λ ¬q) ↔ ¬(p ∨ q)

It is possible to apply De Morgan’s laws to the relationship between two sets as well. Rewrite De Morgan’s laws using our set operators.

3           Writing a Model and representing Propositions (20 pts)

Below is a short passage with several sentences. Create a model populated with the named individuals, and with definitions of all of the predicates used below.  Remember to name the model, create a universe with all of the relevant individuals, and create definitions of both definite descriptors as well as the predicates themselves.  Use correct Set notation to do these definitions.  Ignore things like tense, conjunctions etc.  in the passage; focus on creating a model that is sufficient to determine the meaning of the sentences in this passage.

(6)    Robin introduced June to Nico.  Robin and June are people, but Nico is a fish.  Gregor owns Nico, but Gregor is sick.  Olivia also owns Nico, and Olivia is also sick.  Robin and June are helping Gregor and Olivia. June and Robin will feed Nico.

4            Evaluating Truth of statements relative to a model (14 pts)

Below I will provide you with a Model, M1. The following questions will give you several statements, written in either plain English, or in the syntax of Predicate Logic.  You should determine whether these statement are true in the given model, and say very briefly (one or two sentences) how you know, or where you looked to determine this.

•  U = {Hao Xuan , Kaz , Virgilio , Arshi , Qin Xue , Beng Beng , Osito}

•  [ hIM1  = Hao Xuan; [ kIM1  = Kaz; [ v IM1  = Virgilio; [ a IM1  = Arshi; [ qIM1  = Qin Xue; [ bIM1  = Beng Beng; [ o IM1  = Osito

•  [ DOG IM1  = {Beng Beng}

•  [ CAT IM1  = {Osito}

•  [ PET IM1  = {Osito, Beng Beng}

•  [ PERSON IM1  = {Hao Xuan, Kaz, Virgilio, Arshi, Qin Xue}

•  [ HAPPY IM1  = {Beng Beng, Osito, Qin Xue, Hao Xuan}

•  [ PHD.STUDENT IM1  = {Kaz , Virgilio , Arshi}

•  [ OWN IM1  = {〈Hao Xuan, Osito〉 , 〈Qin Xue, Beng Beng〉}

•  [ LIKE IM1  = {〈Osito , Hao Xuan〉 , 〈Hao Xuan , Osito〉 , 〈Virgilio , Osito〉 , 〈Kaz , Osito〉 , 〈Arshi ,  Osito〉 , 〈Hao Xuan , Beng Beng〉 , 〈Qin Xue , Beng Beng〉 , 〈Beng Beng , Qin Xue〉 , 〈Beng Beng , Kaz〉

, 〈Beng Beng , Hao Xuan〉 }

4.1       Q1

{x : (x ∈ [DOG]M1) V (x ∈ [CAT]M1)} ∈ [HAPPY]M1

4.2       Q2

|{y : LIKE(o,y) in M1}| > 1

4.3       Q3

If someone owns a pet, they are happy.

4.4       Q4

[PHD.STUDENT]M1 ∈/ [HAPPY]M1

4.5       Q5

Virgilio likes every pet.

4.6       Q6

[PHD.STUDENT]M1  ≤ {x : LIKE(x,o) in M1}

4.7       Q7

Beng Beng likes the owner of Osito, but Osito does not like the owner of Beng Beng.