# Math 108: Discrete Mathematics

• Course type: Self-paced
• Available Lessons: 88
• Average Lesson Length: 8 min
• Eligible for Credit: Yes

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### Course Summary

Math 108: Discrete Mathematics has been evaluated and recommended for 3 semester hours and may be transferred to over 2,000 colleges and universities. With this self-paced course, you get engaging lessons, expert instructors who make even the most challenging math and computer science topics simple, and an excellent resource for getting a head start on your degree.
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#### 11 chapters in Math 108: Discrete Mathematics

Course Practice Test

Check your knowledge of this course with a 50-question practice test.
• Comprehensive test covering all topics
• Detailed video explanations for wrong answers
Week {{::cp.getGoalWeekForTopic(0, 11)}}
Ch 1. Introduction to Logic & Proofs {{cp.topicAssetIdToProgress[470875].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - Critical Thinking and Logic in Mathematics
Score: {{cp.lessonAssetIdToProgress[2372].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[2372].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice
Score: {{cp.lessonAssetIdToProgress[2422].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[2422].bestScoreQuestions}}  Take Quiz Optional
Lesson 3 - Logical Fallacies: Appeals to Ignorance, Emotion or Popularity
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Lesson 4 - Propositions, Truth Values and Truth Tables
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Lesson 5 - Logical Math Connectors: Conjunctions and Disjunctions
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Lesson 6 - Conditional Statements in Math
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Lesson 7 - Logic Laws: Converse, Inverse, Contrapositive & Counterexample
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Lesson 8 - Direct Proofs: Definition and Applications
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Lesson 9 - Tautology in Math: Definition & Examples
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Week {{::cp.getGoalWeekForTopic(1, 11)}}
Ch 2. Sets & Functions in Discrete Math {{cp.topicAssetIdToProgress[470877].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - Mathematical Sets: Elements, Intersections & Unions
Score: {{cp.lessonAssetIdToProgress[2378].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[2378].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - Universal Set in Math: Definition, Example & Symbol
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Lesson 3 - Complement of a Set in Math: Definition & Examples
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Lesson 4 - Cardinality & Types of Subsets (Infinite, Finite, Equal, Empty)
Score: {{cp.lessonAssetIdToProgress[2379].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[2379].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Partially Ordered Sets & Lattices in Discrete Mathematics
Score: {{cp.lessonAssetIdToProgress[470879].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470879].bestScoreQuestions}}  Take Quiz Optional
Lesson 6 - What is a Function: Basics and Key Terms
Score: {{cp.lessonAssetIdToProgress[154].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[154].bestScoreQuestions}}  Take Quiz Optional
Lesson 7 - Injections, Surjections & Bijections
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Week {{::cp.getGoalWeekForTopic(2, 11)}}
Ch 3. Sequences, Sums & Induction {{cp.topicAssetIdToProgress[470881].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - What is a Mathematical Sequence?
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Lesson 2 - Introduction to Sequences: Finite and Infinite
Score: {{cp.lessonAssetIdToProgress[18808].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[18808].bestScoreQuestions}}  Take Quiz Optional
Lesson 3 - How to Find and Classify an Arithmetic Sequence
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Lesson 4 - Finding and Classifying Geometric Sequences
Score: {{cp.lessonAssetIdToProgress[635].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[635].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Summation Notation and Mathematical Series
Score: {{cp.lessonAssetIdToProgress[636].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[636].bestScoreQuestions}}  Take Quiz Optional
Lesson 6 - How to Calculate an Arithmetic Series
Score: {{cp.lessonAssetIdToProgress[637].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[637].bestScoreQuestions}}  Take Quiz Optional
Lesson 7 - How to Calculate a Geometric Series
Score: {{cp.lessonAssetIdToProgress[639].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[639].bestScoreQuestions}}  Take Quiz Optional
Lesson 8 - Arithmetic and Geometric Series: Practice Problems
Score: {{cp.lessonAssetIdToProgress[1303].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[1303].bestScoreQuestions}}  Take Quiz Optional
Lesson 9 - Mathematical Induction: Uses & Proofs
Score: {{cp.lessonAssetIdToProgress[18821].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[18821].bestScoreQuestions}}  Take Quiz Optional
Lesson 10 - Proof by Induction: Steps & Examples
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Week {{::cp.getGoalWeekForTopic(3, 11)}}
Ch 4. Counting Rules, Combinations & Permutations {{cp.topicAssetIdToProgress[470883].percentComplete}}% complete
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Lesson 1 - Calculating Possible Outcomes: Definition & Formula
Score: {{cp.lessonAssetIdToProgress[9132].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[9132].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - Combinatorics & the Pigeonhole Principle
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Lesson 3 - How to Calculate a Permutation
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Lesson 4 - How to Calculate the Probability of Permutations
Score: {{cp.lessonAssetIdToProgress[2398].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[2398].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Circular Permutation: Formula & Examples
Score: {{cp.lessonAssetIdToProgress[28056].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[28056].bestScoreQuestions}}  Take Quiz Optional
Lesson 6 - Math Combinations: Formula and Example Problems
Score: {{cp.lessonAssetIdToProgress[2395].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[2395].bestScoreQuestions}}  Take Quiz Optional
Lesson 7 - How to Calculate the Probability of Combinations
Score: {{cp.lessonAssetIdToProgress[2396].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[2396].bestScoreQuestions}}  Take Quiz Optional
Week {{::cp.getGoalWeekForTopic(4, 11)}}
Ch 5. Discrete Probability {{cp.topicAssetIdToProgress[470885].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - Random Variables: Definition, Types & Examples
Score: {{cp.lessonAssetIdToProgress[14796].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14796].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - Finding & Interpreting the Expected Value of a Discrete Random Variable
Score: {{cp.lessonAssetIdToProgress[14798].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14798].bestScoreQuestions}}  Take Quiz Optional
Lesson 3 - Developing Discrete Probability Distributions Theoretically & Finding Expected Values
Score: {{cp.lessonAssetIdToProgress[14799].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14799].bestScoreQuestions}}  Take Quiz Optional
Lesson 4 - Developing Discrete Probability Distributions Empirically & Finding Expected Values
Score: {{cp.lessonAssetIdToProgress[14800].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14800].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Dice: Finding Expected Values of Games of Chance
Score: {{cp.lessonAssetIdToProgress[20963].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[20963].bestScoreQuestions}}  Take Quiz Optional
Lesson 6 - Blackjack: Finding Expected Values of Games of Chance with Cards
Score: {{cp.lessonAssetIdToProgress[21104].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[21104].bestScoreQuestions}}  Take Quiz Optional
Lesson 7 - Poker: Finding Expected Values of High Hands
Score: {{cp.lessonAssetIdToProgress[63808].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[63808].bestScoreQuestions}}  Take Quiz Optional
Lesson 8 - Poker: Finding Expected Values of Low Hands
Score: {{cp.lessonAssetIdToProgress[63809].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[63809].bestScoreQuestions}}  Take Quiz Optional
Lesson 9 - Lotteries: Finding Expected Values of Games of Chance
Score: {{cp.lessonAssetIdToProgress[20964].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[20964].bestScoreQuestions}}  Take Quiz Optional
Lesson 10 - Comparing Game Strategies Using Expected Values: Process & Examples
Score: {{cp.lessonAssetIdToProgress[14802].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14802].bestScoreQuestions}}  Take Quiz Optional
Lesson 11 - How to Apply Discrete Probability Concepts to Problem Solving
Score: {{cp.lessonAssetIdToProgress[14803].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14803].bestScoreQuestions}}  Take Quiz Optional
Week {{::cp.getGoalWeekForTopic(5, 11)}}
Ch 6. Binomial Probability {{cp.topicAssetIdToProgress[470887].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - Binomial Experiments: Definition, Characteristics & Examples
Score: {{cp.lessonAssetIdToProgress[14805].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14805].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - Finding Binomial Probabilities Using Formulas: Process & Examples
Score: {{cp.lessonAssetIdToProgress[14806].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14806].bestScoreQuestions}}  Take Quiz Optional
Lesson 3 - Practice Problems for Finding Binomial Probabilities Using Formulas
Score: {{cp.lessonAssetIdToProgress[14807].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14807].bestScoreQuestions}}  Take Quiz Optional
Lesson 4 - Finding Binomial Probabilities Using Tables
Score: {{cp.lessonAssetIdToProgress[14808].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14808].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Mean & Standard Deviation of a Binomial Random Variable: Formula & Example
Score: {{cp.lessonAssetIdToProgress[14809].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14809].bestScoreQuestions}}  Take Quiz Optional
Lesson 6 - Solving Problems with Binomial Experiments: Steps & Example
Score: {{cp.lessonAssetIdToProgress[14810].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14810].bestScoreQuestions}}  Take Quiz Optional
Week {{::cp.getGoalWeekForTopic(6, 11)}}
Ch 7. Recursion & Advanced Counting {{cp.topicAssetIdToProgress[470889].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - Recursive Functions: Definition & Examples
Score: {{cp.lessonAssetIdToProgress[147450].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[147450].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - What is a First-Order Linear Recurrence? - Definition & Uses
Score: {{cp.lessonAssetIdToProgress[304301].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[304301].bestScoreQuestions}}  Take Quiz Optional
Lesson 3 - How to Solve Linear Recurrence Relations
Score: {{cp.lessonAssetIdToProgress[470891].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470891].bestScoreQuestions}}  Take Quiz Optional
Lesson 4 - Solving Divide-and-Conquer Recurrences
Score: {{cp.lessonAssetIdToProgress[470893].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470893].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Generating Function in Discrete Math: Definition & Examples
Score: {{cp.lessonAssetIdToProgress[470895].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470895].bestScoreQuestions}}  Take Quiz Optional
Lesson 6 - Inclusion-Exclusion Principle in Combinatorics
Score: {{cp.lessonAssetIdToProgress[344373].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[344373].bestScoreQuestions}}  Take Quiz Optional
Week {{::cp.getGoalWeekForTopic(7, 11)}}
Ch 8. Principles of Graphs & Graph Theory {{cp.topicAssetIdToProgress[470897].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - Introduction to Graph Theory
Score: {{cp.lessonAssetIdToProgress[32186].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[32186].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - Graph Theory Concepts and Terminology
Score: {{cp.lessonAssetIdToProgress[32187].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[32187].bestScoreQuestions}}  Take Quiz Optional
Lesson 3 - Graphs in Discrete Math: Definition, Types & Uses
Score: {{cp.lessonAssetIdToProgress[435069].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[435069].bestScoreQuestions}}  Take Quiz Optional
Lesson 4 - Isomorphism & Homomorphism in Graphs
Score: {{cp.lessonAssetIdToProgress[470899].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470899].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Euler Paths and Euler's Circuits
Score: {{cp.lessonAssetIdToProgress[32188].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[32188].bestScoreQuestions}}  Take Quiz Optional
Lesson 6 - Mathematical Models of Euler's Circuits & Euler's Paths
Score: {{cp.lessonAssetIdToProgress[32189].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[32189].bestScoreQuestions}}  Take Quiz Optional
Lesson 7 - Fleury's Algorithm for Finding an Euler Circuit
Score: {{cp.lessonAssetIdToProgress[32191].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[32191].bestScoreQuestions}}  Take Quiz Optional
Lesson 8 - Euler's Theorems: Circuit, Path & Sum of Degrees
Score: {{cp.lessonAssetIdToProgress[32190].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[32190].bestScoreQuestions}}  Take Quiz Optional
Lesson 9 - Eulerizing Graphs in Math
Score: {{cp.lessonAssetIdToProgress[32192].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[32192].bestScoreQuestions}}  Take Quiz Optional
Lesson 10 - Hamilton Circuits and Hamilton Paths
Score: {{cp.lessonAssetIdToProgress[32193].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[32193].bestScoreQuestions}}  Take Quiz Optional
Lesson 11 - Assessing Weighted & Complete Graphs for Hamilton Circuits
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Lesson 12 - Methods of Finding the Most Efficient Circuit
Score: {{cp.lessonAssetIdToProgress[32196].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[32196].bestScoreQuestions}}  Take Quiz Optional
Lesson 13 - Coloring & Traversing Graphs in Discrete Math
Score: {{cp.lessonAssetIdToProgress[470901].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470901].bestScoreQuestions}}  Take Quiz Optional
Lesson 14 - Adjacency Representations of Graphs in Discrete Math
Score: {{cp.lessonAssetIdToProgress[470903].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470903].bestScoreQuestions}}  Take Quiz Optional
Week {{::cp.getGoalWeekForTopic(8, 11)}}
Ch 9. Trees in Discrete Mathematics {{cp.topicAssetIdToProgress[470905].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - What are Trees in Discrete Math? - Definition, Types & Examples
Score: {{cp.lessonAssetIdToProgress[470907].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470907].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - How to Traverse Trees in Discrete Mathematics
Score: {{cp.lessonAssetIdToProgress[470909].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470909].bestScoreQuestions}}  Take Quiz Optional
Lesson 3 - Using Trees for Sorting: Benefits & Disadvantages
Score: {{cp.lessonAssetIdToProgress[470911].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470911].bestScoreQuestions}}  Take Quiz Optional
Lesson 4 - What is a Spanning Tree? - Properties & Applications
Score: {{cp.lessonAssetIdToProgress[470913].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470913].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Minimum Spanning Tree: Algorithms & Examples
Score: {{cp.lessonAssetIdToProgress[470915].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470915].bestScoreQuestions}}  Take Quiz Optional
Week {{::cp.getGoalWeekForTopic(9, 11)}}
Ch 10. Matrices in Discrete Math {{cp.topicAssetIdToProgress[470917].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - What is a Matrix?
Score: {{cp.lessonAssetIdToProgress[561].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[561].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - Matrix Notation, Equal Matrices & Math Operations with Matrices
Score: {{cp.lessonAssetIdToProgress[21231].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[21231].bestScoreQuestions}}  Take Quiz Optional
Lesson 3 - How to Solve Inverse Matrices
Score: {{cp.lessonAssetIdToProgress[21232].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[21232].bestScoreQuestions}}  Take Quiz Optional
Lesson 4 - Using Matrices to Complete Rotations
Score: {{cp.lessonAssetIdToProgress[147388].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[147388].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Using Matrices to Complete Translations
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Week {{::cp.getGoalWeekForTopic(10, 11)}}
Ch 11. Boolean Algebra & Logic Gates {{cp.topicAssetIdToProgress[470919].percentComplete}}% complete
Course Progress Best Score
Lesson 1 - What Is Boolean Logic? - Definition, Diagram & Examples
Score: {{cp.lessonAssetIdToProgress[7776].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[7776].bestScoreQuestions}}  Take Quiz Optional
Lesson 2 - Boolean Algebra: Rules, Theorems, Properties & Examples
Score: {{cp.lessonAssetIdToProgress[20266].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[20266].bestScoreQuestions}}  Take Quiz Optional
Lesson 3 - Boolean Logic, Operators & Expressions
Score: {{cp.lessonAssetIdToProgress[14069].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[14069].bestScoreQuestions}}  Take Quiz Optional
Lesson 4 - What is a Karnaugh Map? - Definition & Examples
Score: {{cp.lessonAssetIdToProgress[344367].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[344367].bestScoreQuestions}}  Take Quiz Optional
Lesson 5 - Arithmetic Logic Unit (ALU): Definition, Design & Function
Score: {{cp.lessonAssetIdToProgress[5532].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[5532].bestScoreQuestions}}  Take Quiz Optional
Lesson 6 - How to Design Logic Circuits & Logic Gates
Score: {{cp.lessonAssetIdToProgress[470921].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470921].bestScoreQuestions}}  Take Quiz Optional
Lesson 7 - NAND, NOR & XOR Logic Gates
Score: {{cp.lessonAssetIdToProgress[470923].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470923].bestScoreQuestions}}  Take Quiz Optional
Lesson 8 - How to Simplify & Combine Logic Circuits
Score: {{cp.lessonAssetIdToProgress[470925].bestScoreCorrect}}/{{cp.lessonAssetIdToProgress[470925].bestScoreQuestions}}  Take Quiz Optional
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 A College Accelerator Study.com membership. Completed the entire Math 108: Discrete Mathematics course and achieved 100% Course Progress. Not attempted to take this exam within the last three days. Have available proctored exams in this month of membership. Complete the exam readiness quiz.

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Practice Tests in this course
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