# 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.