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 (A AND B) when both A and B are true?

Back

The truth value is True.

Front

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

Back

The truth value is False.

Front

What is the result of NOT A when A is True?

Back

The result is False.

Front

What does a truth table for the implication (A → B) show when A is True and B is False?

Back

The truth value is False.

Front

What is the truth value of A AND (B OR C) when A is True, B is False, and C is True?

Back

The truth value is True.

Front

How can truth tables be used in logical reasoning?

Back

Truth tables can be used to evaluate the validity of logical arguments and to determine the truth values of complex expressions.

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.