# Not boolean operation in Excel

In Excel if I have some boolean operation of the form

``````{=SUM(IF((A1:A8="Google")*(B1:B8="Stanford")+(C1:C8="Columbia"),1,0))}
``````

I know that `*` means `AND()` and `+` means `OR()` so that we are searching for ones in columns A and B being "Google" and "Stanford" respectively or those in column C being "Columbia".

But is there a symbol for `NOT()`?

• Excel has `AND()`, `OR()`, and `NOT()` functions, are these useful to you? – Tom Carpenter Nov 13 '15 at 2:08
• No. If I replace the inside of the IF with OR(AND(A:A,B:B),C:C) abbreviating the arguments, then it will not work. I am looking for a symbol representing NOT(), if it exists, that I can use in something like the above expression. – domoremath Nov 13 '15 at 3:00

`*` works as `AND()` and `+` works as `OR()` because `TRUE` has a value of `1` and `FALSE` has a value of `0`.  And, since the `NOT()` function turns `TRUE` into `FALSE` and vice versa (`1``0`), a simple way of implementing `NOT(x)` arithmetically is `1-x`.

Unfortunately, that works only for `0` and `1`.  If you’re using `+` for `OR()`, and you have two (or more) TRUE conditions combined in an expression, you will get a value of `2` or greater.  The good news (which you already know) is that any non-zero number counts as `TRUE`.  The bad news is that `1-2` is `-1`, which is non-zero and hence also `TRUE`.

An alternative solution is the logical expression `x=0`, e.g.,

``````(((A1:A8="Google")*(B1:B8="Stanford")+(C1:C8="Columbia"))=0)
``````

If `x` is `0`, this logical expression evaluates as `TRUE`.  If `x` is anything other than `0`, the expression evaluates as `FALSE`.  Thus, `x=0` functions as `NOT(x)`.

Warning: if you combine multiple Boolean (`TRUE` or `FALSE`) values with `*`, `+`, and `-`, they are converted into integers (numbers); but if you do a `number=number` test, you end up with a Boolean.  Thus, you could say something like

``````=SUM((A1:A8="Google")*(B1:B8="Stanford"))
``````

(without using `IF()`), because `Boolean*Boolean` is a number, but you cannot do

``````=SUM(((A1:A8="Google")*(B1:B8="Stanford"))=0)
``````

because `SUM()` does not work on Boolean values.  But you can use it

• in an `IF()`,
• by adding 0 (`+0`), or
• by multiplying by 1 (`*1`).