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Boolean logical operators - AND, OR, NOT, XOR

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The logical Boolean operators perform logical operations with bool operands. The operators include the unary logical negation (!), binary logical AND (&), OR (|), and exclusive OR (^), and the binary conditional logical AND (&&) and OR (||).

For operands of the integral numeric types, the &, |, and ^ operators perform bitwise logical operations. For more information, see Bitwise and shift operators.

Logical negation operator !

The unary prefix ! operator computes logical negation of its operand. That is, it produces true, if the operand evaluates to false, and false, if the operand evaluates to true:

bool passed = false;
Console.WriteLine(!passed);  // output: True
Console.WriteLine(!true);    // output: False

The unary postfix ! operator is the null-forgiving operator.

Logical AND operator &

The & operator computes the logical AND of its operands. The result of x & y is true if both x and y evaluate to true. Otherwise, the result is false.

The & operator always evaluates both operands. When the left-hand operand evaluates to false, the operation result is false regardless of the value of the right-hand operand. However, even then, the right-hand operand is evaluated.

In the following example, the right-hand operand of the & operator is a method call, which is performed regardless of the value of the left-hand operand:

bool SecondOperand()
{
    Console.WriteLine("Second operand is evaluated.");
    return true;
}

bool a = false & SecondOperand();
Console.WriteLine(a);
// Output:
// Second operand is evaluated.
// False

bool b = true & SecondOperand();
Console.WriteLine(b);
// Output:
// Second operand is evaluated.
// True

The conditional logical AND operator && also computes the logical AND of its operands, but doesn't evaluate the right-hand operand if the left-hand operand evaluates to false.

For operands of the integral numeric types, the & operator computes the bitwise logical AND of its operands. The unary & operator is the address-of operator.

Logical exclusive OR operator ^

The ^ operator computes the logical exclusive OR, also known as the logical XOR, of its operands. The result of x ^ y is true if x evaluates to true and y evaluates to false, or x evaluates to false and y evaluates to true. Otherwise, the result is false. That is, for the bool operands, the ^ operator computes the same result as the inequality operator !=.

Console.WriteLine(true ^ true);    // output: False
Console.WriteLine(true ^ false);   // output: True
Console.WriteLine(false ^ true);   // output: True
Console.WriteLine(false ^ false);  // output: False

For operands of the integral numeric types, the ^ operator computes the bitwise logical exclusive OR of its operands.

Logical OR operator |

The | operator computes the logical OR of its operands. The result of x | y is true if either x or y evaluates to true. Otherwise, the result is false.

The | operator always evaluates both operands. When the left-hand operand evaluates to true, the operation result is true regardless of the value of the right-hand operand. However, even then, the right-hand operand is evaluated.

In the following example, the right-hand operand of the | operator is a method call, which is performed regardless of the value of the left-hand operand:

bool SecondOperand()
{
    Console.WriteLine("Second operand is evaluated.");
    return true;
}

bool a = true | SecondOperand();
Console.WriteLine(a);
// Output:
// Second operand is evaluated.
// True

bool b = false | SecondOperand();
Console.WriteLine(b);
// Output:
// Second operand is evaluated.
// True

The conditional logical OR operator || also computes the logical OR of its operands, but doesn't evaluate the right-hand operand if the left-hand operand evaluates to true.

For operands of the integral numeric types, the | operator computes the bitwise logical OR of its operands.

Conditional logical AND operator &&

The conditional logical AND operator &&, also known as the "short-circuiting" logical AND operator, computes the logical AND of its operands. The result of x && y is true if both x and y evaluate to true. Otherwise, the result is false. If x evaluates to false, y isn't evaluated.

In the following example, the right-hand operand of the && operator is a method call, which isn't performed if the left-hand operand evaluates to false:

bool SecondOperand()
{
    Console.WriteLine("Second operand is evaluated.");
    return true;
}

bool a = false && SecondOperand();
Console.WriteLine(a);
// Output:
// False

bool b = true && SecondOperand();
Console.WriteLine(b);
// Output:
// Second operand is evaluated.
// True

The logical AND operator & also computes the logical AND of its operands, but always evaluates both operands.

Conditional logical OR operator ||

The conditional logical OR operator ||, also known as the "short-circuiting" logical OR operator, computes the logical OR of its operands. The result of x || y is true if either x or y evaluates to true. Otherwise, the result is false. If x evaluates to true, y isn't evaluated.

In the following example, the right-hand operand of the || operator is a method call, which isn't performed if the left-hand operand evaluates to true:

bool SecondOperand()
{
    Console.WriteLine("Second operand is evaluated.");
    return true;
}

bool a = true || SecondOperand();
Console.WriteLine(a);
// Output:
// True

bool b = false || SecondOperand();
Console.WriteLine(b);
// Output:
// Second operand is evaluated.
// True

The logical OR operator | also computes the logical OR of its operands, but always evaluates both operands.

Nullable Boolean logical operators

For bool? operands, the & (logical AND) and | (logical OR) operators support the three-valued logic as follows:

  • The & operator produces true only if both its operands evaluate to true. If either x or y evaluates to false, x & y produces false (even if another operand evaluates to null). Otherwise, the result of x & y is null.

  • The | operator produces false only if both its operands evaluate to false. If either x or y evaluates to true, x | y produces true (even if another operand evaluates to null). Otherwise, the result of x | y is null.

The following table presents that semantics:

x y x&y x|y
true true true true
true false false true
true null null true
false true false true
false false false false
false null false null
null true null true
null false false null
null null null null

The behavior of those operators differs from the typical operator behavior with nullable value types. Typically, an operator that is defined for operands of a value type can be also used with operands of the corresponding nullable value type. Such an operator produces null if any of its operands evaluates to null. However, the & and | operators can produce non-null even if one of the operands evaluates to null. For more information about the operator behavior with nullable value types, see the Lifted operators section of the Nullable value types article.

You can also use the ! and ^ operators with bool? operands, as the following example shows:

bool? test = null;
Display(!test);         // output: null
Display(test ^ false);  // output: null
Display(test ^ null);   // output: null
Display(true ^ null);   // output: null

void Display(bool? b) => Console.WriteLine(b is null ? "null" : b.Value.ToString());

The conditional logical operators && and || don't support bool? operands.

Compound assignment

For a binary operator op, a compound assignment expression of the form

x op= y

is equivalent to

x = x op y

except that x is only evaluated once.

The &, |, and ^ operators support compound assignment, as the following example shows:

bool test = true;
test &= false;
Console.WriteLine(test);  // output: False

test |= true;
Console.WriteLine(test);  // output: True

test ^= false;
Console.WriteLine(test);  // output: True

Note

The conditional logical operators && and || don't support compound assignment.

Operator precedence

The following list orders logical operators starting from the highest precedence to the lowest:

  • Logical negation operator !
  • Logical AND operator &
  • Logical exclusive OR operator ^
  • Logical OR operator |
  • Conditional logical AND operator &&
  • Conditional logical OR operator ||

Use parentheses, (), to change the order of evaluation imposed by operator precedence:

Console.WriteLine(true | true & false);   // output: True
Console.WriteLine((true | true) & false); // output: False

bool Operand(string name, bool value)
{
    Console.WriteLine($"Operand {name} is evaluated.");
    return value;
}

var byDefaultPrecedence = Operand("A", true) || Operand("B", true) && Operand("C", false);
Console.WriteLine(byDefaultPrecedence);
// Output:
// Operand A is evaluated.
// True

var changedOrder = (Operand("A", true) || Operand("B", true)) && Operand("C", false);
Console.WriteLine(changedOrder);
// Output:
// Operand A is evaluated.
// Operand C is evaluated.
// False

For the complete list of C# operators ordered by precedence level, see the Operator precedence section of the C# operators article.

Operator overloadability

A user-defined type can overload the !, &, |, and ^ operators. When a binary operator is overloaded, the corresponding compound assignment operator is also implicitly overloaded. A user-defined type can't explicitly overload a compound assignment operator.

A user-defined type can't overload the conditional logical operators && and ||. However, if a user-defined type overloads the true and false operators and the & or | operator in a certain way, the && or || operation, respectively, can be evaluated for the operands of that type. For more information, see the User-defined conditional logical operators section of the C# language specification.

C# language specification

For more information, see the following sections of the C# language specification:

See also