Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
What is symbolic logic?
What is symbolic logic?
A system using symbols and variables to represent statements and logical operations.
Which of the following represents the inverse?
Which of the following represents the inverse?
- ∼q → ∼p
- p ∧ q
- p → q
- ∼p → ∼q (correct)
What does the biconditional (↔) indicate?
What does the biconditional (↔) indicate?
- p if and only if q (correct)
- If p, then q
- p and q are both true
- p or q
A disjunction (p ∨ q) implies that both p and q must be true.
A disjunction (p ∨ q) implies that both p and q must be true.
Signup and view all the answers
What does negation (∼) indicate?
What does negation (∼) indicate?
Signup and view all the answers
What is a compound statement?
What is a compound statement?
Signup and view all the answers
What is reflection symmetry?
What is reflection symmetry?
Signup and view all the answers
A conditional statement has only one form.
A conditional statement has only one form.
Signup and view all the answers
Flashcards are hidden until you start studying
Study Notes
Symbolic Logic Overview
- Symbolic Logic utilizes symbols and variables to denote statements and logical operations.
- A statement is defined as an assertion that can be classified as either true or false.
Types of Statements
- Simple Statement: A statement with no components; stands alone.
- Compound Statement: Combines two or more simple statements through logical connectives.
Logical Connectives
- Negation (∼): Indicates the opposite truth value of a statement.
- Conjunction (∧): "p and q" is true only if both p and q are true.
- Disjunction (∨): "p or q" is true if at least one of p or q is true.
- Conditional (→): "If p, then q" states that if p is true, q must also be true.
- Biconditional (↔): "p if and only if q" requires both statements to have the same truth value.
Truth Tables
- Truth tables enumerate the possible truth values for logical expressions and help evaluate compound statements.
Examples of Compound Statements
-
Example statements involving Harry:
- h: Harry is not happy.
- v: Harry is going to watch a volleyball game.
- r: It is going to rain.
- s: Today is Sunday.
-
Various compound statements can be formed such as:
- s ∧ ∼h: Today is Sunday and Harry is not happy.
- s ∧ ∼v: Today is Sunday and Harry is not watching volleyball.
- r → ∼v: If it is going to rain, then Harry is not watching volleyball.
Conditional Statements and Their Forms
- A conditional statement (p → q) has two derived forms:
- Converse: q → p
- Inverse: ∼p → ∼q
- Contrapositive: ∼q → ∼p
Equivalence in Statements
- Two statements are equivalent if they yield the same truth values.
- Parentheses in compound statements clarify the application order of connectives.
Patterns Overview
- A pattern is a repeatable structure or design prevalent in nature, human-made constructs, or abstract concepts.
Symmetry
- Reflection Symmetry (Mirror Symmetry): A figure that can be split into two identical halves.
- Translation Symmetry: Represents a pattern that can be moved or translated without altering its appearance.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
