1. Mathematical Statements
- A declarative sentence that is either True or False (not both)
- Example: “2 + 2 = 4” (True) | “2 + 2 = 5” (False)
2. Logical Connectives
- Negation (¬) : NOT — flips truth value
- Conjunction (∧) : AND — true only if both are true
- Disjunction (∨) : OR — true if at least one is true
3. Conditional and Bi-conditional
- Conditional (→) : “If p, then q” — false only when p is true and q is false
- Bi-conditional (↔) : “p if and only if q” — true when p and q have same truth value
4. Truth Tables and Tautologies
- Truth Table: Lists truth values of compound statements for all possible inputs
- Tautology: Statement that is always true (e.g., p ∨ ¬p)
5. Quantifiers
- Universal (∀) : “For all” / “For every”
- Existential (∃) : “There exists” / “For some”
6. Logical Implication and Equivalence
- Implication (⇒) : p implies q if p → q is always true
- Equivalence (≡) : p and q have same truth value in all cases
7. Deductive Reasoning
- Drawing conclusions from premises using valid arguments
- If premises are true and logic is valid, conclusion must be true