Truth Tables

Front

What is a truth table?

Back

A truth table is a mathematical table used to determine the truth values of logical expressions based on their inputs.

Front

What are the basic logical operators used in truth tables?

Back

The basic logical operators are AND (∧), OR (∨), NOT (¬), and IMPLIES (→).

Front

How many rows does a truth table have for n variables?

Back

A truth table for n variables has 2^n rows.

Front

What is the truth value of a conjunction (AND) when one operand is false?

Back

The truth value of a conjunction is false if at least one operand is false.

Front

What is the truth value of a disjunction (OR) when both operands are false?

Back

The truth value of a disjunction is false if both operands are false.

Front

What does the NOT operator do in a truth table?

Back

The NOT operator inverts the truth value of a proposition; if the proposition is true, it becomes false, and vice versa.

Front

What is the truth value of an implication (A → B) when A is true and B is false?

Back

The truth value of the implication A → B is false when A is true and B is false.

Front

What is a tautology in the context of truth tables?

Back

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

Front

What is a contradiction in the context of truth tables?

Back

A contradiction is a logical statement that is always false regardless of the truth values of its components.

Front

How can truth tables be used to evaluate logical expressions?

Back

Truth tables can be used to systematically evaluate the truth values of logical expressions by listing all possible combinations of truth values for the variables.