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Propositional Logic - Coggle Diagram
Propositional Logic
5. Inference Rules
- If P → Q and P are true, then Q is true.
- If P → Q and ¬Q are true, then ¬P is true.
- Hypothetical Syllogism: If P → Q and Q → R, then P → R.
- Disjunctive Syllogism: If P ∨ Q and ¬P, then Q.
6. Proof Techniques
- Demonstrating the truth of a proposition by a straightforward chain of logical steps.
- Proof by Contradiction: Assuming the negation of the proposition and deriving a contradiction.
- Assuming the antecedent of an implication and deriving the consequent.
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2. Basic Elements
- Statements that can be either true or false.
- Examples: "It is raining," "2 + 2 = 4."
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- IF AND ONLY IF (↔): Biconditional
3. Syntax and Semantics
- Rules for constructing valid expressions in propositional logic.
- Tool for determining the truth value of propositions and logical expressions.
4. Logical Equivalences
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- P ∧ (Q ∨ R) ≡ (P ∧ Q) ∨ (P ∧ R)
- (P ∧ Q) ∧ R ≡ P ∧ (Q ∧ R)
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- Simplification of Expressions
- Using equivalences to reduce the complexity of logical formulas.
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