Back To Course

Math 102: College Mathematics14 chapters | 108 lessons

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.

If Judy likes all things round, then Judy will love donuts.

This is a logical statement. **Logic** is the study of how to critically think about propositions or statements that are either true or false. The statement I just made about Judy came about from thinking critically about the proposition that Judy likes all things round and about donuts. I know the proposition that Judy likes all things round is true, and I know the proposition that donuts are round is true, as well. Because both propositions are true, I can link them together to reach the conclusion that Judy will love donuts because donuts are round. This is the way logic works.

Logic is very useful in the world of mathematics. Mathematicians use logic all the time to prove theorems and other mathematical facts. Everything we know about math right now is based off of these logical proofs. Without these, we wouldn't have our formulas, like the wonderful quadratic formula or the very useful Pythagorean Theorem.

Using logic in math is about mixing the specific language used in logic with the specific symbols used in math. Let me show you.

In logic, **propositions** are simple statements that can either be true or false. Your propositions don't have to be complicated. They can be short ones like, 'All squares are yellow,' or 'Judy likes all things pink.' Your proposition is any statement that can be labeled as either true or false.

Logic propositions in math usually include math symbols. In geometry, you can have a proposition that says, 'Line AB is the bisector of line CD' with the corresponding math symbol for lines instead of the word 'line.' In algebra, your proposition can be as simple as *x* = 2. Depending on what kind of math you're working with, you can have a mixture of words with math symbols or all math symbols. What matters most is that your logic proposition can be labeled as either true or false.

Usually, your problem will tell you whether a statement is true or false. One thing to keep in mind here is that if your problem says something is true, you have to believe that. Don't over think the statement. If you see a statement such as 2 + 2 = 5, and the problem says that it is true, then you have to believe that and work with it, but only for that problem. I know it might be hard to do, but what is true and false in logic does not have to make sense in the real world.

Let's now see how we can apply logic and critical thinking to a problem.

Once we are given our propositions, we need to use our critical thinking skills to come up with conclusions. Critical thinking involves creating new connections using what we know is true. For example, let's say that our problem tells us that *x* = 5 and *y* = 1 are true propositions. What kind of new statements and connections can we make?

We can say that, 'If *z* = *x* + *y*, then *z* = 6' because 5 + 1 = 6. We can also say something like, 'If *z* = *x* * *y*, then *z* = 5.' Do you see how we are creating new connections from what we know to be true? We use the if-then structure to write our new connections.

In review, **logic** is the study of how to critically think about propositions or statements that are either true or false. In math, the logic statements can involve just words, words and symbols together or just symbols. A logic **proposition** is simply a statement that can be labeled as either true or false. You use critical thinking to make new connections based on what you know to be true. You write your new connections in the form of an if-then statement.

After you've completed this lesson, you'll be able to:

- Define logic and proposition
- Explain how to use critical thinking and logic in math to make new connections

To unlock this lesson you must be a Study.com Member.

Create your account

Already a member? Log In

BackDid you know… We have over 79 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
1 in chapter 11 of the course:

Back To Course

Math 102: College Mathematics14 chapters | 108 lessons

- Critical Thinking and Logic in Mathematics 4:27
- Logical Fallacies: Appeals to Ignorance, Emotion or Popularity 8:53
- Propositions, Truth Values and Truth Tables 9:49
- Logical Math Connectors: Conjunctions and Disjunctions 3:39
- Conditional Statements in Math 4:54
- Logic Laws: Converse, Inverse, Contrapositive & Counterexample 7:09
- Go to Logic

- Go to Sets

- Go to Geometry

- PECT PreK-4: Practice & Study Guide
- ISEE Middle Level: Practice & Study Guide
- ISEE Lower Level: Practice & Study Guide
- ISEE Upper Level: Practice & Study Guide
- California Red Cross Nurse Assistant Competency Evaluation (CNA Test) Training
- Database Management & Data Analytics
- Impact of Lipids on Nutrition
- The Role of Vitamins in Nutrition
- How the Body Handles Nutrients
- Role of Physical Fitness in Nutrition
- What Are WIDA Standards?
- WIDA Can Do Descriptors for Kindergarten
- Demographics for English Language Learners
- Is the TAP Test Hard?
- What is Professional Development for Teachers?
- MTEL Content Test Requirements
- How to Earn Kanban Certification

- Multiple Costing: Definition & Calculation
- Brand Strength & Pricing in Hospitality & Tourism
- Classroom Activities for Introverts
- The Black Legend: Definition & History
- Bermuda Triangle Lesson Plan
- ESL Making Arrangements Vocabulary
- How to Change Your Name: Laws & Process
- Working With Linear Formulas
- Quiz & Worksheet - How Teachers & Administrators Collaborate
- Quiz & Worksheet - Using a Child's Interests to Promote Learning
- Quiz & Worksheet - Analyzing Email Campaigns
- Quiz & Worksheet - Behavioral Theories in Business Communication
- Quiz & Worksheet - Reggio Emilia Educational Approach
- Graphing & Evaluating Equations & Functions Flashcards
- Exponential & Logarithmic Function Flashcards

- 8th Grade Language Arts: Lessons & Help
- MTEL Physics: Practice & Study Guide
- Assessment of Learning for Teachers
- PLACE Business Education: Practice & Study Guide
- Ohio Assessments for Educators - Middle Grades English Language Arts: Practice & Study Guide
- Western Civilization Since 1945
- TExES Business Education: Ethics
- Quiz & Worksheet - Hallucination Types & Causes
- Quiz & Worksheet - Finding Cause and Effect of an Event in Literature
- Quiz & Worksheet - Features of Diary Entries
- Quiz & Worksheet - Ancient Persian Art and Architecture
- Quiz & Worksheet - Interpreting a Speech

- Regression To The Mean in Psychology: Definition & Example
- Recursively Using Stages of the Writing Process
- How to Pass the Series 6 Exam
- eBooks vs. Textbooks
- Common Core Standards in Maine
- How to Study for the DSST
- Teacher Appreciation Day Ideas
- What are the NYS Regents Exams Locations?
- EPT Test Dates
- Student Loan Forgiveness for Teachers in Texas
- Telling Time Lesson Plan
- Multiplication Games for Kids

Browse by subject