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Questions and Answers
What is symbolic logic?
A system using symbols and variables to represent statements and logical operations.
Which of the following represents the inverse?
What does the biconditional (↔) indicate?
A disjunction (p ∨ q) implies that both p and q must be true.
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What does negation (∼) indicate?
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What is a compound statement?
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What is reflection symmetry?
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A conditional statement has only one form.
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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
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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.
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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.
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Description
This quiz provides an overview of symbolic logic, covering key concepts such as inverse, contrapositive, and converse. It discusses how symbols and variables are used to represent statements and logical operations. Perfect for those looking to understand the foundations of symbolic logic.
