Podcast
Questions and Answers
What percentage of the total grade is allocated to the Final Exam?
What percentage of the total grade is allocated to the Final Exam?
Which of the following topics is NOT covered in the course?
Which of the following topics is NOT covered in the course?
What is the title of the textbook used for the course?
What is the title of the textbook used for the course?
What edition of the textbook is specified for the course?
What edition of the textbook is specified for the course?
Signup and view all the answers
How much of the assessment is based on Mid-Term Exam performance?
How much of the assessment is based on Mid-Term Exam performance?
Signup and view all the answers
Which week does the content cover for the Fall Semester?
Which week does the content cover for the Fall Semester?
Signup and view all the answers
Which assessment method has the highest weight in this course?
Which assessment method has the highest weight in this course?
Signup and view all the answers
Which of the following is an activity assessed in the course?
Which of the following is an activity assessed in the course?
Signup and view all the answers
Which course code is assigned to Discrete Structures?
Which course code is assigned to Discrete Structures?
Signup and view all the answers
What should students use as a study guide?
What should students use as a study guide?
Signup and view all the answers
Study Notes
Course Information
- Course Title: Information Technology
- Subject: Discrete Mathematics
- Course Code: MA 112
- Semester: Fall 2023-2024
- Textbook: Discrete Mathematics and its Applications by K. Rosen, 8th Edition
- Course Website URL: Provided
- Instructor Information: E-mail and office location are provided
Course Topics
- Sets and Set Operations
- Functions
- Relations
- Mathematical Induction
- Propositional Logic
- Proof Techniques
- Graphs
- Trees
Assessment Method
- Assignments: 20%
- Quizzes: 20%
- Tutorial and Lab Attendance/Performance/Interaction: 50%
- Mid-Term Exam: 50%
- Final Exam: 100%
Propositional Logic
- Propositional logic is the study of relationships between objects
- Propositional Logic forms the basis of mathematical reasoning and automated reasoning.
- Proposition: Declarative sentences that are either true or false.
- Examples of propositions:
- Cairo is the capital of Egypt (True)
- 1 + 1 = 2 (True)
- 2 + 2 = 3 (False)
- What is not a proposition:
- What time is it (question)
- Read this carefully (instruction)
Logical Connectives
- Negation (¬): The opposite of a statement.
- Conjunction (∧): Combining statements with "and".
- Disjunction (∨): Combining statements with "or".
- Exclusive OR (⊕): Combining statements where only one is true, not both.
- Conditional (→): Combining statements using "if-then".
- Biconditional (↔): Combining statements with "if and only if".
Conditional Statements
- Hypothesis/Antecedent/Premise
- Conclusion/Consequence
- Converse: Switching the hypothesis and conclusion.
- Inverse: Negating both hypothesis and conclusion in original statement.
- Contrapositive: Switching the hypothesis and conclusion, and negating both, in original statement.
- There are many ways to express conditional statements
Truth Tables
- Truth tables are used to show the truth or falsity of logical statements
- Shows the truth values of a compound proposition
Logical Equivalences
- Equivalent expressions have the same truth values under all possible circumstance.
- Rules/laws are used to show/prove logical equivalence
Laws of Logic
- Commutative laws
- Associative laws
- Distributive laws
- Identity laws
- Complement laws
- De Morgan's Laws
Predicates and Quantifiers
- Predicates are statements that are either true or false.
- Quantifiers are operators used to limit the variables of a predicate.
- Universal Quantifier (∀): For all elements of a set.
- Existential Quantifier (∃): There exists an element of a set.
- Important definitions, examples, ways to negate statements
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
