# Microsoft Excel – Logical Functions – AND, OR and XOR formulas

I have explained a few logical functions in the Article “Microsoft Excel – Logical Functions – IF, IFERROR and IFNA formulas“. In this article, we will go through another set of logical functions AND, OR, and XOR. All of these formulas take multiple arguments; the first argument is mandatory and the other arguments are optional.

All of these formulas will return a logical value either TRUE or FALSE unless there is no Error.

### `AND` function

The syntax of `AND` formula is:

`=AND(argument 1, [argument 2], ...)`

Where arguments are logical values or numeric values or the logical expressions or even references to the Cells. The first argument is a must and the rest are optional.

`AND` formula checks whether all of its arguments are TRUE; then returns the logical value TRUE. Otherwise, this function returns the logical value FALSE.

 Formula Result =AND(TRUE, TRUE) TRUE =AND(TRUE, FALSE) FALSE =AND(FALSE, FALSE) FALSE

### `OR` function

`OR` function verifies whether one of its arguments is TRUE and returns the logical value TRUE. Else, this formula returns the logical value FALSE.

The Syntax of the `OR` function is:

`=OR(argument 1, [argument 2], ...)`

Unlike `AND` formula `OR` formula returns the logical value TRUE if any of its arguments is TRUE or all arguments are TRUE.

 Formula Result =OR(TRUE, TRUE) TRUE =OR(TRUE, FALSE) TRUE =OR(FALSE, FALSE) FALSE

### `XOR` function

`XOR` function returns the logical “Exclusive OR” of all of its arguments. This is a bit tricky to understand. To simplify, if you pass two arguments to `XOR` formula; it returns the value TRUE, ONLY when one of its arguments is TRUE and the other argument is FALSE.

The Syntax of the `XOR` function is:

`=XOR(argument 1, [argument 2], ...)`

When we pass multiple arguments to this function, how do we know which logical value this function returns? Let’s take an example:

`=XOR(TRUE, FALSE, TRUE)`

The above formula returns the value, FALSE. Because, XOR of the first two arguments returns the value TRUE; then XOR of TRUE, TRUE returns the value FALSE.

To easy to remember, XOR returns the logical value TRUE; if its arguments contain an odd number of TRUE inputs. Otherwise, this function returns the value FALSE.

 Formula Result =XOR(TRUE, TRUE) FALSE =XOR(TRUE, FALSE) TRUE =XOR(FALSE, FALSE) FALSE

All of these functions are NOT allowed to pass text as an argument. If you pass text, these functions return “#VALUE!” Error.

We discuss more on Excel through upcoming Articles.

🙂 Sahida

Microsoft Excel – Logical Functions – AND, OR and XOR formulas
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