Formal Logic
- Formal System of rules for how we should prove or disprove things
- Can be used to represent the statments that we use in English to communicate facts or information
Statements
A sentence that is true or false NOT both
Truth Value
True = T(1)
False n= F(0)
Compound Statements
Statement made of more than one simple statement
- Usually use some kind of logical connectives
Components of Compound Statements
- Statement Variables : A, B, C
- Logical Connectives: ∨, ∧, →, ↔, ¬
Conjuction
∧ (AND)
A ∧ B : “A and B”
Disjuction
OR
A ∨ B: “A or B”
Negation
¬ NOT
¬ A : “Not A”
Implication
→ IF
A → B : “If A then B” or “A implies B”
A : Hypothesis
B : Conclusion
Equivalence
↔ If and only if
A ↔ B : “A if and only if B”
Well formed formulas (WFF)
Combined variables, connectives, and parentheses make an expression that is meaningful.
Order of Precedence
- Connectives parentheses, innermost parenthese first
- Negation
- Conjuction, disjunction
- Implication
- Equivalence
Number of Rows in a Truth Table
2^n
Tautology
A wff that is intrinsically true, no matter what statements comprise the wff
Contradictions
A wff that is intrisically false, no matter what the truth statements that compromise the wff
Propostions
Also known as statements.
Logical Equivalences
Two statements forms are logically equivalent if and only if they have identical truth values for each possible substitution of statements for their statement variables.
Denotes 𝑃 ≡ 𝑄
- Used to simplify statements
