Calculate Truth Value
Enter a logical expression and assign values to variables to calculate the result.
Understanding Truth Value Calculation
Truth value calculation determines whether a logical expression is true or false for specific assignments of truth values to its variables. This is fundamental to logical evaluation and forms the basis of all logical reasoning. For more on truth values in logic, see Stanford Encyclopedia of Philosophy.
Key Concepts
- Variables: Represent propositions that can be true or false
- Operators: Combine variables according to logical rules - see Khan Academy's logical operators guide
- Evaluation: Process of determining the final truth value
- Assignment: Specific values given to variables
How Truth Value Calculation Works
The calculator parses the expression, identifies variables, allows value assignment, and evaluates the result.
Process Steps
- Parse the logical expression
- Extract variable names
- Create input controls for each variable
- Apply assigned values to variables
- Evaluate the expression step by step
- Return the final truth value
Detailed Examples
Example 1: A ∧ B
Expression: A ∧ B
| Assignment | Calculation | Result |
|---|---|---|
| A=T, B=T | T ∧ T | T |
| A=T, B=F | T ∧ F | F |
| A=F, B=T | F ∧ T | F |
| A=F, B=F | F ∧ F | F |
Example 2: A ∨ ¬B
Expression: A ∨ ¬B
| Assignment | ¬B | A ∨ ¬B | Result |
|---|---|---|---|
| A=T, B=T | ¬T = F | T ∨ F | T |
| A=T, B=F | ¬F = T | T ∨ T | T |
| A=F, B=T | ¬T = F | F ∨ F | F |
| A=F, B=F | ¬F = T | F ∨ T | T |
Operator Truth Tables
AND (∧) Operator
| A | B | A ∧ B |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
OR (∨) Operator
| A | B | A ∨ B |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
NOT (¬) Operator
| A | ¬A |
|---|---|
| T | F |
| F | T |
Complex Expression Evaluation
For complex expressions, evaluation follows operator precedence and associativity rules.
Precedence Order
- NOT (¬)
- AND (∧)
- OR (∨)
- IMPLIES (→)
- BICONDITIONAL (↔)
Example: (A ∧ B) ∨ (¬C)
Assignment: A=T, B=F, C=T
- A ∧ B = T ∧ F = F
- ¬C = ¬T = F
- (A ∧ B) ∨ (¬C) = F ∨ F = F