Logical Functions
This category contains the Logical functions.
Handling nonlogical arguments in logical functions

Zero (0) is equivalent to FALSE and all other numbers are equivalent to TRUE.

Empty cells and text in cells are ignored.

A #VALUE error is raised if all arguments are ignored.

A #VALUE error is raised if one argument is direct text (not text in a cell).

Errors as argument lead to an error.
AND
Returns TRUE if all arguments are TRUE. If one of the elements is FALSE, this function returns the FALSE value.
The arguments are either logical expressions themselves (TRUE, 1<5, 2+3=7, B8<10) that return logical values, or arrays (A1:C3) containing logical values.
AND(LogicalValue1; LogicalValue2 ...LogicalValue30)
LogicalValue1; LogicalValue2 ...LogicalValue30 are conditions to be checked. All conditions can be either TRUE or FALSE. If a range is entered as a parameter, the function uses all values of the range. The result is TRUE if the logical value in all cells within the cell range is TRUE.
The logical values of entries 12<13; 14>12, and 7<6 are to be checked:
=AND(12<13;14>12;7<6) returns FALSE.
=AND (FALSE;TRUE) returns FALSE.
FALSE
Returns the logical value FALSE. The FALSE() function does not require any arguments, and always returns the logical value FALSE.
FALSE()
=FALSE() returns FALSE
=NOT(FALSE()) returns TRUE
IF
Specifies a logical test to be performed.
IF(Test; ThenValue; OtherwiseValue)
Test is any value or expression that can be TRUE or FALSE.
ThenValue (optional) is the value that is returned if the logical test is TRUE.
OtherwiseValue (optional) is the value that is returned if the logical test is FALSE.
In the LibreOffice Calc functions, parameters marked as "optional" can be left out only when no parameter follows. For example, in a function with four parameters, where the last two parameters are marked as "optional", you can leave out parameter 4 or parameters 3 and 4, but you cannot leave out parameter 3 alone.
=IF(A1>5;100;"too small") If the value in A1 is higher than 5, the value 100 is entered in the current cell; otherwise, the text â€śtoo smallâ€ť (without quotes) is entered.
NOT
Complements (inverts) a logical value.
NOT(LogicalValue)
LogicalValue is any value to be complemented.
=NOT(A). If A=TRUE then NOT(A) will evaluate FALSE.
OR
Returns TRUE if at least one argument is TRUE. This function returns the value FALSE, if all the arguments have the logical value FALSE.
The arguments are either logical expressions themselves (TRUE, 1<5, 2+3=7, B8<10) that return logical values, or arrays (A1:C3) containing logical values.
OR(LogicalValue1; LogicalValue2 ...LogicalValue30)
LogicalValue1; LogicalValue2 ...LogicalValue30 are conditions to be checked. All conditions can be either TRUE or FALSE. If a range is entered as a parameter, the function uses all values of the range.
The logical values of entries 12<11; 13>22, and 45=45 are to be checked.
=OR(12<11;13>22;45=45) returns TRUE.
=OR(FALSE;TRUE) returns TRUE.
TRUE
The logical value is set to TRUE. The TRUE() function does not require any arguments, and always returns the logical value TRUE.
TRUE()
If A=TRUE and B=FALSE the following examples appear:
=AND(A;B) returns FALSE
=OR(A;B) returns TRUE
=NOT(AND(A;B)) returns TRUE
XOR
Returns true if an odd number of arguments evaluates to TRUE.
The arguments are either logical expressions themselves (TRUE, 1<5, 2+3=7, B8<10) that return logical values, or arrays (A1:C3) containing logical values.
XOR(LogicalValue1; LogicalValue2 ...LogicalValue30)
=XOR(TRUE;TRUE) returns FALSE
=XOR(TRUE;TRUE;TRUE) returns TRUE
=XOR(FALSE;TRUE) returns TRUE