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 its operand.

Front

What is the result of the implication (A → B) when A is true and B is false?

Back

The result of the implication is false when A is true and B is false.

Front

How do you represent a tautology in a truth table?

Back

A tautology is represented in a truth table by having all rows evaluate to true.

Front

What is a contradiction in the context of truth tables?

Back

A contradiction is represented in a truth table by having all rows evaluate to false.

Front

What is the significance of the last column in a truth table?

Back

The last column in a truth table shows the final truth value of the logical expression for all combinations of input values.