# Boolean Logical Operators Truth Table

Boolean logical operators is just a fancy name for the language used to combine multiple condition formulas into a single condition formula or, in the case of the `NOT()`

function, reverse the results of a condition formula.

`AND`

, `OR`

and `NOT()`

have similar meanings as in conversational English. Both `a AND b`

need to be true for the result to be true. Either `a OR b`

can be true for its result to be true. `NOT(b)`

is only true if b is false.

The rest of the Boolean Logical Operators can all be created by combining those three operators. For example, `a NOR b`

is the same as `NOT(a OR b)`

, but it is shorter to write using `NOR`

.

The following true table explains the results when different combinations of true and false formulas are used as the inputs of the various logical operators.

Inputs | True | Mixed | False | |
---|---|---|---|---|

`a AND b` |
And | True | False | False |

`a OR b` |
Inclusive Or | True | True | False |

`NOT(b)` |
Not | False | True | |

`a NAND b` |
Not And | False | True | True |

`a NOR b` |
Not Inclusive Or | False | False | True |

`a XNOR b` |
Not Exclusive Or | True | False | True |

`a XOR b` |
Exclusive Or | False | True | False |

Where `a`

and `b`

are both Boolean formulas (returning true or false).

The order of `a`

and `b`

do not matter.

The `NOT()`

function just takes one Boolean formula and reverses its result. This is why it does not have a result listed for Mixed.