Truth table

Definition

A truth table is a mathematical table used to determine if a logical expression is true or false under all possible interpretations. It lists all possible combinations of inputs and their corresponding output values for the expression.

5 Must Know Facts For Your Next Test

1. Truth tables are used to evaluate logical expressions involving AND, OR, and NOT operators.
2. Each row in a truth table represents a unique combination of truth values for the variables involved.
3. A truth table for an expression with n variables has 2^n rows.
4. Truth tables help identify tautologies, contradictions, and contingencies in logical statements.
5. They are essential tools in digital logic design and computer science.

Review Questions

• How many rows does a truth table have for an expression with three variables?
• What logical operators are commonly evaluated using truth tables?
• What can you determine about an expression if its truth table shows the output as true for all input combinations?

Related terms

Logical Expression: A combination of symbols and operators that represent a specific logic operation.

Tautology:

A logical statement that is always true, regardless of the truth values of its components.

Contradiction:

A logical statement that is always false, no matter what the truth values of its components are.