Logic: Statements, Connectives and Truth Tables
A logical statement is a declarative sentence with a definite truth value: true or false. Questions, commands, and open sentences with unspecified variables are not statements.
Summary
A logical statement is a declarative sentence with a definite truth value: true or false. Questions, commands, and open sentences with unspecified variables are not statements. Compound statements depend on their component statements and the connectives joining them. Negation, , reverses the truth value of .
| Connective | When the compound statement is true |
|---|---|
| Conjunction, | Both components are true |
| Inclusive disjunction, |
🧠 Key Concepts
- Logical statements
- Negation
- Conjunction
- Inclusive disjunction
- Conditional
- Biconditional
- Truth table rows
- Tautology
- Contradiction
- Argument validity
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Logic: Statements, Connectives and Truth Tables
📘 Overview A logical statement has a definite truth value: true or false. Logical connectives combine or modify statements, and truth tables show the resulting truth value for every possible assignment to the component statements.
🧠 Key Idea The truth value of a compound statement depends on its component statements and the connectives joining them. A truth table systematically checks every possible combination rather than relying on everyday interpretations of words such as "or" and "if."
⚔️ Core Details: - A statement is a declarative sentence that is either true or false; questions, commands, and open sentences with unspecified variables are not statements. - Negation, , reverses the truth value of the statement . - Conjunction,
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