about_Logical_Operators
SHORT DESCRIPTION
Describes the operators that connect statements in PowerShell.
LONG DESCRIPTION
The PowerShell logical operators connect expressions and statements, allowing you to use a single expression to test for multiple conditions.
For example, the following statement uses the and operator and the or operator to connect three conditional statements. The statement is true only when the value of $a is greater than the value of $b, and either $a or $b is less than 20.
($a gt $b) and (($a lt 20) or ($b lt 20))
PowerShell supports the following logical operators.
Operator  Description  Example 

and 
Logical AND. TRUE when both  (1 eq 1) and (1 eq 2) 
statements are TRUE.  False 

or 
Logical OR. TRUE when either  (1 eq 1) or (1 eq 2) 
statement is TRUE.  True 

xor 
Logical EXCLUSIVE OR. TRUE when  (1 eq 1) xor (2 eq 2) 
only one statement is TRUE  False 

not 
Logical not. Negates the statement  not (1 eq 1) 
that follows.  False 

! 
Same as not 
!(1 eq 1) 
False 
Note:
The previous examples also use the equal to comparison operator eq
. For
more information, see
about_Comparison_Operators. The examples also
use the Boolean values of integers. The integer 0 has a value of FALSE. All
other integers have a value of TRUE.
The syntax of the logical operators is as follows:
<statement> {AND  OR  XOR} <statement>
{!  NOT} <statement>
Statements that use the logical operators return Boolean (TRUE or FALSE) values.
The PowerShell logical operators evaluate only the statements required to
determine the truth value of the statement. If the left operand in a statement
that contains the and operator is FALSE, the right operand is not evaluated.
If the left operand in a statement that contains the or statement is TRUE, the
right operand is not evaluated. As a result, you can use these statements in
the same way that you would use the If
statement.