Truth Tables and Basic Boolean Algebra A truth table is a tabular representation of all possible combinations of truth values of three or more variables. A...
Truth Tables and Basic Boolean Algebra
A truth table is a tabular representation of all possible combinations of truth values of three or more variables. A variable can be either True or False. A truth table is used to determine the truth value of a compound proposition, which is a statement that is true if and only if all of its variables are true.
The basic operators of Boolean algebra are AND (∧), OR (∨), and NOT (¬).
AND is a logical operator that is used to combine two or more propositions using the operator "and". For example, the statement "x AND y" is true if both x and y are true.
OR is a logical operator that is used to combine two or more propositions using the operator "or". For example, the statement "x OR y" is true if either x or y is true.
NOT is a logical operator that is used to combine two or more propositions using the operator "not". For example, the statement "¬x" is true if x is false.
Truth tables provide a systematic way to determine the truth value of compound propositions. By combining propositions using the logical operators, we can build up complex propositions that represent real-world situations.
Examples
| x | y | x AND y |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
| x | y | x OR y |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
| x | ¬x |
|---|---|
| T | F |
| F | T |