Truth Table is a table that shows the truth value (true or false) of a #202204281244. It takes \(2^n\) steps to display all truth values, where \(n\) is the number of variables involved.
Negation
The \(\sim p\) or \(\neg p\) truth value is shown as below:
| \(p\) | \(\sim p\) |
|---|---|
| T | F |
| F | T |
Conjunction
The \(p \land q\) truth value is shown as below:
| \(p\) | \(q\) | \(p \land q\) |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
Inclusive Disjunction
The \(p \lor q\) truth value is shown as below:
| \(p\) | \(q\) | \(p \lor q\) |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Exclusive Disjunction
The \(p \oplus q\) truth value is shown as below:
| \(p\) | \(q\) | \(p \oplus q\) |
|---|---|---|
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |
Conditional Statement
The \(p \rightarrow q\) truth value is shown as below:
| \(p\) | \(q\) | \(p \rightarrow q\) |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | T |
| F | F | T |
Biconditional Statement
The \(p \leftrightarrow q\) truth value is shown as below:
| \(p\) | \(q\) | \(p \leftrightarrow q\) |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | T |