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.

True Mixed False
a AND b
And True False False
a OR b
Inclusive Or True True False
Not False
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.