# INTRODUCTION TO SYMBOLIC LOGIC

PHIL012.201 (UP), PHIL012.002 (WD) • Summer 2013 • Online
*All Exams and Quizzes administered via ANGEL

David W. Agler, PhD
Office Hours: TR 8AM–9AM EST
Office Location: Chat (see Yammer & Office Hours below)

e: dwa132@psu.edu
w: www.davidagler.com

1. Course Description
2. Course Overview
3. Course Policies
4. Course Calendar & Best Tips
5. Technical Tutorials

# 1. COURSE DESCRIPTION

## 1.1. COURSE DESCRIPTION

This is an introductory course in symbolic logic. Logic is the science of correct reasoning. Symbolic logic is a particular branch of logic that studies correct reasoning using a formal or artificial language. This course will articulate two different formal languages: propositional logic and predicate logic. In both languages, we will examine how these artificial languages relate to English (a natural language), different ways in which formal languages can be used to determine whether arguments are valid (or invalid), and how to reason using these languages.

## 1.2. PREREQUISITES

While there are no prerequisites for this course, note that this course satisfies a quantitative requirement (GQ) and so any previous experience you have in mathematics (e.g. algebra or geometry in high school) or knowledge of computer languages will help you greatly.

# 2. COURSE OVERVIEW

## 2.1. REQUIRED TEXTS

1. Agler, David W. 2013. Symbolic Logic: Syntax, Semantics, and Proof. Lanham, MA: Rowman & Littlefield. Paperback \$65; eBook: \$65; Hardcover: \$120; ISBN: 978-1-4422-1742-3 (see Amazon and Rowman & Littlefield)
2. Also see handouts for this text, available at: http://davidagler.com/teaching/logic.html

## 2.2. COURSE OBJECTIVES

• Critical Reasoning Skills: Students will learn certain fundamental features of language and argument analysis, which will allow them to identify arguments, isolate the premises and conclusion of these arguments, and represent language using a formal language.
• Analytical Reasoning Skills: Students will develop a specialized set of skills that will allow them to translate arguments into and reason with a formal language. This language will also allow them to mechanically determine various logical properties of sentences, sets of sentences, and arguments.
• Critical Thinking: Students will develop a general set of skills that allow them to analyze and assess a variety of different arguments, deciding whether the arguments are properly supported, fallacious, or valid. In addition, students will learn how to employ various strategies for proving the deductive validity of arguments.
• Dialogue & Expression: Students will engage in respectful conversation with classmates as well as collaborate with their peers to better learn logic. In addition, students will learn how to clearly articulate and represent various arguments as well as convey the process (or strategies) by which certain conclusions are reached.

## 2.3. COURSE WORK

1. Readings and Interactive Materials (ungraded): Each lesson requires a significant amount of reading from the text, and contains additional on-line content and interactive materials. Any questions about any of these materials can be posted to the Yammer PHIL012 Logic Page. Your instructor will check this forum daily.
2. Homework Exercises (5% of final grade): You are required to complete exercises from the textbook and upload them as a file to ANGEL. Exercises are graded in terms of completion rather than on the basis of whether or not they are correct. While there is no precise number of exercises you must complete, in order to receive full credit, you must do all of the following:
• Complete at least five of the exercises from the appropriate chapter, clearly labeling these, e.g. “Chapter 2, Exercise Set #1, A, #4”
• You upload your exercises as a file (preferably PDF) to the Exercise File Dropbox in the Lesson Folder (in ANGEL) before the due date.
• Note: if you submit quizzes or exams as a PDF and using the file-naming procedures found here you will receive 1pt of extra credit on that assignment.
3. Eight Practice Quizzes (10% of final grade): Each lesson will contain a practice quiz that you should take when you have completed the readings, done all the exercises, and gone through all the on-line materials. These are designed to help you assess how prepared you are for the quiz and/or exam for that lesson. These will be graded for completion rather than for correctness.
4. Eight Quizzes (15% of final grade): Most lessons will also contain a quiz covering the material for that lesson. The format of the quiz will vary depending on the subject matter of the lesson, but it will be similar to that of the practice quiz for that lesson. Note: Quizzes will be subject to a time limit. After the time expires, the quiz will be inaccessible and the grade will be calculated based on what is completed so far. Students will be given a warning prior to the time limit. See quiz instructions for details.
5. Five Exams (70% of final grade): There are 5 exams. The format for each exam varies depending on the material covered. No consultation with other students or outside materials is allowed during exam period. Note: Exams will be subject to a time limit. After the time expires, the exam will be inaccessible and the grade will be calculated based on what is completed so far. Students will be given a warning prior to the time limit. See exam instructions for details.
6. Extra Credit: There are several opportunities to acquire extra credit through the course. First, there is extra credit for submitting quizzes and exams with correct file-naming procedures and as PDF (see here).

## 2.4. INSTRUCTOR FEEDBACK & RESPONSE TIME

Getting General Feedback: If you have content-related questions or want to collaborate with your peers, you have three options: (1) via Yammer, you can communicate with your instructor during online office hours using the chat function, (2) via Yammer (see below), you can post questions, comments, and other materials, (3) you can email your instructor. Note: When corresponding with your instructor or classmates, please use appropriate language and etiquette. For the best possible feedback, try to formulate your question or comment as precisely as possible, referring to page numbers, posting what you think the answer might be, etc.

TYPE OF ACTIVITY / ASSESSMENT TYPE OF FEEDBACK PROVIDED TIMEFRAME OF FEEDBACK
Questions via Email I understand that timely feedback is important for doing well in this course. If I cannot provide a detailed response within one business day, I will write to you letting you know when I will be able to address your question. Within 48 hours of email, typically much sooner
Homework Exercises You will receive a grade via ANGEL Within 72 hours of due date
Practice Quizzes All of these (except Practice Quiz #6) are automatically graded. Immediately

## 2.5. OFFICE HOURS

Office Hours: Your instructor will hold office hours via Chat available in Yammer.com. To Sign Up For Yammer: Go to www.yammer.com/psu.edu and using your Penn State ID, join Yammer. Once you have joined yammer, join the “PHIL 012 Symbolic Logic” group. There you will be able to access and post materials, ask questions, and interact with other students taking the course. For a step-by-step tutorial, see the Yammer Tutorial in this syllabus. Why Use Yammer: If you have a question about the content of the course, I prefer that you post it via Yammer. Yammer offers you a more dynamic and public way to receive feedback from your instructor and your peers. If you have questions about specific exercises, concepts, definitions, proofs, terms, don’t hesitate, post it to Yammer!

# 3. COURSE POLICIES

## 3.1. ACADEMIC MISCONDUCT

The general principles and policy relating to cheating and plagiarism, which are enforced in this class, can be found in the Penn State policy on academic misconduct. Academic Integrity: Academic dishonesty encompasses a wide range of activities, whether intentional or unintentional, that includes, but is not limited to: all forms of fraud, plagiarism, and any failure to cite explicitly all materials and sources used in one’s work. Sanctions for these activities include, but are not limited to, failure in a course, removal from the degree program, failure in a course with an explanation in the permanent transcript of the cause for failure, suspension, and expulsion. If you are unclear about whether you or someone you know is engaging in academic misconduct, read the following: University Statement on Academic Integrity. For more information, see PSU Academic Integrity, PSU ITS, Plagiarism Tutor, & PSU Teaching & Learning with Technology

## 3.2. DEADLINES & LATE WORK

All assignments are due by 11:30PM EST on the assigned date (please refer to the course calendar in the Getting Started folder for due dates). Students will be unable to go back and complete course work; it is your responsibility to keep up with your assignments. Students with an excused absence (hospitalization, jury duty, or family emergencies) may be asked to produce proper documentation in order to make up graded work. All make up work is at the discretion of the instructor.

Late work will only be accepted for Quiz #1 and Lesson #1 Exercises. The penalty for turning these two assessments in late is a letter grade deduction for every day that the assessment is late. After the first week of the course, no late work will be accepted. Please keep in mind that the window in which you can submit a variety of assignments is large, e.g. a week to turn in the Lesson #1 Exercises, so do not wait until the last minute to turn in your assignments.

## 3.3. TECHNICAL SUPPORT

There are a number of ways to receive technical support:

• For UP Students: contact the ITS Help Desk through their website (http://itservicedesk.psu.edu) by phone (814-865-HELP (4357) or via email (ITShelpdesk@psu.edu).
• For World Campus Students: contact the Outreach Help Desk through their website (http://student.worldcampus.psu.edu/technical-support), by phone 1-800-252-3592, option 4 (toll free within the United States) or 1-814-865-0047 (local and international calls) or via email (ohd@psu.edu)
• For both UP and WD students: the “I Need Technical Assistance …” message board can be used to communicate specific questions or problems. Students are encouraged to respond to the problems and questions posted there by their peers. To access ANGEL’s technical support page, click on the Help button (in the image of a question mark), found on the left of the screen in ANGEL. Turnaround time is generally less than one business day.

## 3.4. GRADE ROUNDING

Grades will be rounded up from the second decimal point, e.g. 90.95 rounds up to 91.0 while 90.94 rounds down to 90.90. In the event that eLION does not allow for a particular grade (e.g. D+), you will simply be given the letter grade (e.g. if you have a D+ then you will receive a D, and if you have a C–, you will receive a C).

A: 91–100%;
A–: 90.0–90.9
B+: 89.0–89.9
B: 81.0–88.9
B–: 80–80.9
C+: 79.0–79.9
C: 71.0–78.9
C–: 70–70.9
D+: 69.0–69.9
D: 60.0–68.9
F: 0–59.9
INCOMPLETE
DROP

Note: While ANGEL provides a rough approximation of your grade, the syllabus is the definitive guide for determining your grade. Please use the percentages in the Course Work section to determine your grade.

## 3.5. ACCESSIBILITY STATEMENT & FURTHER STUDENT GUIDANCE

Penn State welcomes students with disabilities into the University's educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact the Office for Disability Services (ODS) at 814-863-1807 (V/TTY). For further information regarding ODS, please visit the Office for Disability Services Web site at: http://equity.psu.edu/ods/.

If you are in need of psychological counseling, please do not hesitate to contact Penn State’s Counseling & Psychological Services (phone: 814-863-0395). For any problem related to your studies, university policies and procedures, do not hesitate to seek the help of the Student Affairs Services, your Academic Advisor, or arrange a meeting with your instructor who will help you obtain assistance through one of the above, or another, agency.

## 3.6. USE OF ANGEL AND EMAIL COMMUNICATION

Please check the webpage on the ANGEL website regularly. An online version of the syllabus is available there, and you will be notified of any cancellation of a course meeting there. If you need to contact me, send a well-constructed email to your instructor’s email address with an appropriate subject line (e.g. PHIL012 Logic Question) and with an appropriate address (e.g. “Dear David”). Failure to do either, or emailing me with multiple links attached (“check this youtube link”) may result in your email being inadvertently deleted. Students are responsible for activity on their computer accounts so only send emails pertinent to the course. Also, please try not to send correspondence from cellular telephones (e.g. Blackberries, etc.).

Concerning email correspondence, there are some practices to keep in mind if you want optimal feedback.

• Be sure to use your PSU email address, address me as the recipient, and include your name as the sender. This ensures your email does not wind up in a junk folder.
• Be sure to include helpful specifics, e.g. the problem number, the page number of the problem, and any solutions you may have tried.

Here is a sample email (for more on best email practices, see syllabus):

Dear David,

I am in your PHIL012 World Campus course and am working on problem #A.1 from page 43.
This problem asks how to translate "John is tall and Frank is tall" in the language of PL. I translated this as "F^J" but the solution on page 45 gives "J^F" as the answer. Is my answer wrong?

Best wishes,
David Agler

## 3.7. TUTORING, DROP PROCEDURES, AND INCOMPLETES

Through the course of the semester, you may decide you need additional tutoring. Occasionally, Penn State Learning offers private tutoring. At their website, go to the “Resources” page, and click “Engage a Private Tutor” to request a tutor for this course. Consult the Register site for drop procedures. Consult the Handbook for taking an Incomplete (D/F).

# 3.8. CHALLENGE EXAMINATION (NOT AVAILABLE IN WEB-VERSION OF COURSE)

In some circumstances, Penn State will allow you to receive credit for a course by examination (Policy 42-50). If you are interested in this, you should contact the relevant academic department or program about whether this is offered.

In rare cases, this course allows for a variation on this called a “challenge exam”. In order to accommodate students who have done poorly in the semester but who have learned the material throughout the course of the semester, you can take what I call a “challenge exam”.

A challenge exam is a difficult comprehensive exam that covers all of the material covered in this course. This includes (but is not limited to):

1. Propositional and predicate logic translation (including advanced translation)
2. Propositional and predicate logic syntax & semantics
3. Propositional and predicate logic trees & tables
4. Propositional and predicate logic proofs

In order to be eligible to take the challenge exam, you must meet all of the following criteria:

1. Complete every assessment for the course (homework, quizzes, exams, etc.)
2. Attend class on a regular basis
3. For every extra credit opportunity, it is necessary that you (i) participated for those that take place in the classroom or (ii) turned in a submission for those that are outside of the classroom.
4. You must formally announce your intent to take the challenge exam before the last assessment of the course. That is, you cannot ask to take the challenge exam after completing the final exam.

On the condition that you meet all of the above conditions and you pass the challenge exam with a 70% or better, you will receive a “C” for the course. You may not take the challenge exam to receive a grade higher than a “C”.

# 4. COURSE CALENDAR & BEST Tips

## 4.1.Course Calendar

Import due dates of assessments to your calendar (Abbreviated Course Calendar ICAL / HTML Version Here). Here is a tutorial on how to import events into your Calendar (Google Calendar Import)

LESSON READING & EXERCISES TECHNICAL SKILLS ASSESSMENTS DUE
Part I: Introduction     All assignments due at 11:30PM EST
Lesson 1: Elements of Logic Read: Chapter 1
Suggested Exercises:
Ex Set #1, pp.12-13: A. 1-5, B. 1-5
End-of-Chapter Exercises, p.20-22: A.1-5, B.1-5, C.1-5
Yammer
Best Practices for File Types & File Names
Upload PDF to dropbox
Exercise Files #1: 6/30
Practice Quiz #1: 6/30
Quiz #1: 6/30
Part II: Propositional Logic
Lesson 2: Syntax & Semantics Read: Chapter 2
Suggested Exercises:
Ex Set #1, pp.43-45: A. 1-5, B. 1-5, C. 1-5, D. 1-5
End-of-Chapter Exercises, pp.58-60: A. 1-5, B. 1-5, C. 1-5, D. 1-7, E. 1-5, F. 1-5, G. 1-3
Logic in MSWORD (Webapps)
How to Input & Hotkey Logical Symbols
Exercise Files #2: 7/7
Practice Quiz #2: 7/7
Quiz #2: 7/7
Lesson 3: Truth Tables Read: Chapter 3
Suggested Exercises:
Ex Set #1, pp.68: A.1-7
Ex Set #2, pp.74: A.1-5
Ex Set #3, pp.80: A.1-5
End-of-Chapter Exercises, pp.92-94: A.1-3, B.1-3, C.1-3, D.1-3
How to Make a Truth Table in Word Exercise Files #3: 7/7
Practice Quiz #3: 7/7
Quiz #3: 7/7
Exam #1: 7/9
Lesson 4: Truth Trees Read: Chapter 4
Suggested Exercises:
Ex Set #2, pp.118-119: A. 1-7
Ex Set #3, pp.125: A. 1-7
Ex Set #4, pp.132: A. 1-5
Ex Set #5, pp.141-142: A. 1-3
End-of-Chapter Exercises, pp.150-151: A.1-3, B.1-3, C.1-3, D.1-5
How to Make a Truth Tree in Word Exercise Files #4: 7/14
Practice Quiz #4: 7/14
Quiz #4: 7/14
Exam #2: 7/16
Lesson 5: Derivations Read: Chapter 5
Suggested Exercises:
Ex Set #1, pp.168: A.1-5
Ex Set #2, pp.180: A. 1-5, 9
Ex Set #3, pp.182: A.1-5
Ex Set #4, pp.189-190: A.1-7, B. 1-3
Ex Set #5, pp.198: A.1-3
Ex Set #6, pp.206-7: A. 1-5, B. 1-5
End-of-Chapter Exercises, pp.223-241: Easy 1-5, Medium 34-39, Hard 67-73, Zero-Premise 102-111,
Conceptual and Application Exercises 1-2
How to Solve a Proof in Word Exercise Files #5: 7/21
Practice Quiz #5: 7/21
Quiz #5: 7/21
Exam #3: 7/23
Part III: Predicate Logic
Lesson 6: Syntax & Semantics Read: Chapter 6
Suggested Exercises:
Ex Set #1, pp.255: A. 1-7
Ex Set #2, pp.261-262: A. 1-5, B. 1-5, C. 1-5
Ex Set #3, pp.269: A. 1-5, B. 1-5
Ex Set #4, pp.276: A.1-5
Ex Set #5, pp.280-281: A. 1-5, B. 1-5
How to use the HTML Editor in ANGEL Exercise Files #6: 7/28
Practice Quiz #6: 7/28
Quiz #6: 7/28
Lesson 7: Trees Read: Chapter 7
Suggested Exercises:
Ex Set #1, pp.292: A. 1-5
Ex Set #2, pp.302: A. 1-5
Ex Set #3, pp.307-308: A.1-3
Ex Set #4, pp.311: A.1-3
Ex Set #5, pp.316: A.1-5

Exercise Files #7: 7/28
Practice Quiz #7: 7/28
Quiz #7: 7/28
Exam #4: 7/30
Lesson 8: Derivations Read: Chapter 8
Suggested Exercises:
Ex Set #1, pp.333: A. 1-5
Ex Set #2, pp.346: A. 1-7
End-of-Chapter Exercises, pp.352: A. 1-7, B. 1-7
Exercise Files #8: 8/4
Practice Quiz #8: 8/4
Quiz #8: 8/4
Exam #5: 8/9
Note that this schedule is subject to revision, but all changes will be announced via email.

## 4.2. Tip #1: Spend Extra Time Preparing for Lessons #4 and #5

Notice in the chart above that students do much better on Exam #1 (Lessons #1-#3) than they do on Exams #2-#5 (Lessons #4-#8). What is likely the case is that the first few lessons give the impression that the rest of the course is of the same difficulty. But, as you can see from the above chart, the course becomes more difficult. So, prepare accordingly.

## 4.3. Tip #2: Do the Quizzes in Advance

There is a correlation between how well you do on a quiz and how well you do on an exam. This is becaues the content on the quizzes is very similar to the content on exams. But, you will notice that some students did better on exams than they did on quizzes. Quizzes offer me an opportunity to give you feedback before you take the exam, so take the quizzes early so you can look over my comments and prepare for the exam accordingly.

# 5. TECHNICAL TUTORIALS

## 5.1. YAMMER

Yammer is a social networking tool at PSU. We will use this tool to collaborate, ask questions about content, and to share information that will help you succeed in this course. To Get Started:

Step #1. Go to Yammer at yammer.psu.edu and click the “Log In” button. Yammer is behind WebAccess so you will log in with your PSU User ID, e.g. “xyz132” and password). You won’t need to sign up for anything new!

Step #2. Next, you should feel free to create a profile (optional) just like you would in Facebook. What is important though is that you get access to the Symbolic Logic Group. So search “PHIL012 Symbolic Logic” in the Search Bar at the top of the page.

Step #3. The group is private & so you will have to wait until you are approved. Once you are approved, the first place you should access the Introduction to Symbolic Logic Note and respond to the prompt there. To find this, click on PHIL012 Symbolic Logic in the Groups Sidebar, then click on Notes.

Finally, you may want to adjust how Yammer contacts you. I you are getting bombarded with emails, there is a way to turn this off. Here is how: Go to the little silhouette of a person in the upper right corner, click “Edit Account”, then click “Notifications”, then you can set the type of notifications you receive. If you don’t want any emails, you can unclick all.

## 5.2. BEST PRACTICES FOR FILE TYPES & FILE NAMES

Following certain practices for choosing file types (.pdf as opposed to .doc) and file names will allow you and others to readily identify, access, and organize your work. In this course, you run the risk of not receiving credit for your work if you don’t follow the procedures below.

Rule #1: Avoid periods, and certain characters like \ / ? * & { } [ ] ”, .

Certain characters that are not easily readable or that serve specific functions should be avoided in the name of your file. Periods are used at the end of file names to indicate the format of a file.

Correct: exam3_agler.pdf
Incorrect: exam.3?agler.pdf

If you use one these characters, you or an intended recipient might not be able to open the file.

Rule #2: Use underscores instead of spaces.

On the web, spaces frequently get replaced by the percentage sign “%”. Spaces should thus be avoided because a file named “Quiz 8.doc” can get translated as “Quiz%8.doc” and this can cause confusion in trying to locate your file. If it is necessary to create a space between different characters in your file name, use an underscore. For example, if you want to name your file “Quiz8” but also want to include your last name, you might title it as follows:

Correct: quiz8_agler.pdf
Incorrect: quiz 8.pdf

Rule #3: Use a brief but descriptive name for your file.

The name of your file should contain enough information to (i) allow you to distinguish it from other files you may have and (ii) allow relevant recipients to distinguish it from other files they might receive. Suppose you are taking five courses and each course has a take home quiz that you must email to your instructor. If you title each of these “quiz.doc”, you might mistakenly send your Math quiz to your Biology teacher and your Biology quiz to your Math teacher.

In addition, if Professor Liz receives five files from five different students all named “quiz8.doc”. If Liz doesn’t rename these files, she might not know whose quiz she is grading. For PHIL012, use the name & number of the assessment plus an underscore and your last name in any files you upload. For example, if you uploading a quiz in lesson 5, you should title it as:

Correct: quiz5_lastname.pdf
Incorrect: quiz5.pdf

Rule #4: If you have multiple versions of your file, include a version number.

Finally, it is helpful to save multiple versions of a file. Sometimes files get corrupted, accidently deleted, or you want to distinguish one version of a file from another when communicating with another individual. For this purpose, it is helpful to include use a numbering convention to distinguish versions of the same

Correct: exam1_agler_v001.pdf or exam1_agler_1.pdf

Rule #5: When using special symbols, use PDF

Word processing programs reformat documents every time it is opened on a different computer. This means that how you see your document may not be the same as how your recipient sees it. Page numbers might get reformatted or special symbols that you may use might not appear. Therefore, whenever you submit your work, you should send it as a PDF:

Correct: exam3_agler.pdf
Incorrect: exam3_agler.docx
Incorrect: exam3_agler.pages

If you cannot save your work as a PDF (e.g. MSWord 2007 has an add-in), there are several programs and online options that will allow you to turn your document into a PDF. Here are three:

OxGarage (I recommend this one): www.tei-c.org/oxgarage/
PrimoPDF: www.primopdf.com
Online Primo PDF: www.online.primopdf.com/

Finally, for any quiz or exam requiring a file upload, you will receive +1 for submitting as PDF, for following the above file-naming procedures, and for naming your files as follows:

Scheme: assignmentname#_lastname.pdf
For Exercise Files: homework7_agler.pdf
For Quizzes: quiz5_agler.pdf
For Exams: exam5_agler.pdf

## 5.3. UPLOAD FILE INTO ANGEL DROP BOX

A good deal of your work will require you to upload a file into an ANGEL Drop Box.

Step #1: In the Lesson #1 ANGEL folder, click on “Exercise Files”

Step #2: Title the document you plan on submitting, e.g. “Chapter 1 Exercise Files – [Last Name], and include a message describing what you are submitting. Once you have completed this, click on the Attachments button and a pop-up window will appear.

Step #3: In the pop-up window, click on Browse to search for the file you wish to upload. Once you have found it, click the Upload button, wait a moment, and then click the Finished button.

Step #4: A link to your file should now appear along with your Title and Message. Click the Submit button to submit the file.

## 5.4. LOGIC IN MSWORD (WEBAPPS)

This course will require you to submit your work as a file that displays special “logical” symbols. If you already have a version of MSWord, you can skip to the How to Input & Hotkey Logical Symbols Tutorial. If you don’t own a copy of MSWord or will be working on machines that don’t have this program installed, you do not need to purchase MSWord as Penn State provides a webapp version of it. To access MSWord, please follow the following steps

Step #1. Type the following web address into your browser: http://webapps.psu.edu/ and click on either Office 2010 or Office 2013.

Step#2 Click on the Word icon & sign in with your PSU User name and password

Step #3. Work on your file & save it. Note that you are not saving this file to your computer but to an external server at PSU. Let’s save a file titled “I love logic.docx” to the Desktop.

Step #4 To retrieve this file, type “https://webfiles.psu.edu/” into your browser, locate your file, and download and/or share the file.

In the above example, the “I love logic.docx” is located under the Desktop in the UDrive Personal (V).

## 5.5. HOW TO INPUT & HOTKEY LOGICAL SYMBOLS

Step #1: First, you must learn how to input logical symbols into a document. To do this, watch the How to Input Logical Symbols in MS Word video (especially starting at 1:12)

Step #2: Now that you know how to input logical symbols into a document, you will want to create shortcuts so that you can input the symbol you want with a single keystroke. That is, what you want is to hit “alt+ctrl+6” (or some other combination) and have the "^” symbol appear. To do this, we will need to create a shortcut or hotkey for each symbol you want to use.

First pull up the Insert Symbol Menu. That is, click [Insert, then Symbol, then More Symbols, then Font: Symbol]

Step #3: Select the symbol you want to hotkey. You can find the following symbols under the Symbol font: , , , ,

Step #4: Click the Shortcut Key

Step #5: Enter the shortcut (hotkey) you want in “Press new shortcut key”

Now that you have returned to your word processing document, you should be able to click your keystroke and have your desired symbol appear.

## 5.9. HOW TO USE THE HTML EDITOR

If you can't use the HTML editor (this may be a problem with Java on your computer), then use the following shorthand:

 E existential quantifier A universal quantifier -> conditional v wedge / disjunction ^ carrot / conjunction ~ tilde / negation <-> double arrow / biconditional