# The NAND, NOR, and XOR operators in Python#

The NAND, NOR, and XOR operators are logical operators that are not built into Python, but can be implemented using the built-in not, and, and or operators. The NAND operator returns True if and only if both of its operands are False, and the NOR operator returns True if and only if both of its operands are False. The XOR operator returns True if and only if exactly one of its operands is True.

## The NAND logic operator#

As can be seen in the truth table below, the NAND operator returns True if and only of its operands are False this is the opposite of the and operator. That is because the not operator is applied to the result of the and operator which inverts the result.

A |
B |
Result |
---|---|---|

True |
True |
False |

True |
False |
True |

False |
True |
True |

False |
False |
True |

The NAND operator can be implemented in Python as follows:

```
def nand(a, b):
return not (a and b)
```

If the nand function is called with True and False as its arguments, it will return True because the and operator returns False and the not operator inverts the result. This can also be directly implemented in a Python program as follows:

```
def main():
a = True
b = False
if not (a and b):
print("The NAND of", a, "and", b, "is True")
else:
print("The NAND of", a, "and", b, "is False")
if __name__ == "__main__":
main()
```

## The NOR logic operator#

Like the NAND operator, the NOR operator returns True if and only if both of its operands are False. This is the opposite of the or operator. That is because the not operator is applied to the result of the or operator which inverts the result.

A |
B |
Result |
---|---|---|

True |
True |
False |

True |
False |
False |

False |
True |
False |

False |
False |
True |

The NOR operator can be implemented in Python as follows:

```
def nor(a, b):
return not (a or b)
```

If the nor function is called with True and False as its arguments, it will return False because the or operator returns True and the not operator inverts the result. This can also be directly implemented in a Python program as follows:

```
def main():
a = True
b = False
if not (a or b):
print("The NOR of", a, "and", b, "is True")
else:
print("The NOR of", a, "and", b, "is False")
if __name__ == "__main__":
main()
```

## The XOR logic operator#

Unlike the and and or operators, the XOR operator returns True if and only if exactly one of its operands is True. The truth table for the XOR operator is as follows and it can be implemented using the and, or, and not operators.

A |
B |
Result |
---|---|---|

True |
True |
False |

True |
False |
True |

False |
True |
True |

False |
False |
False |

The XOR operator can be implemented in Python as follows:

```
def xor(a, b):
return (a and not b) or (not a and b)
```

If the xor function is called with True and False as its arguments, it will return True because the first part of the expression (a and not b) returns True and the second part of the expression (not a and b) returns True. This can also be directly implemented in a Python program as follows:

```
def main():
a = True
b = False
if (a and not b) or (not a and b):
print("The XOR of", a, "and", b, "is True")
else:
print("The XOR of", a, "and", b, "is False")
if __name__ == "__main__":
main()
```

Note

The `xor`

function can also be implemented using the `^`

operator as follows:

```
def xor(a, b):
return a ^ b
```

The `^`

operator returns True if and only if exactly one of its operands is True.

Note

The `operator`

module in Python provides a function called xor that can be used to implement the XOR logic as follows:

```
import operator
def xor(a, b):
return operator.xor(a, b)
```

## The XNOR logic operator#

The XNOR operator returns True if and only if both of its operands are True or both of its operands are False. This is the opposite of the XOR operator. The truth table for the XNOR operator is as follows and it can be implemented using the and, or, and not operators.

A |
B |
Result |
---|---|---|

True |
True |
True |

True |
False |
False |

False |
True |
False |

False |
False |
True |

The xnor operator can be implemented in Python as follows:

```
def xnor(a, b):
return (a and b) or (not a and not b)
```

If the xnor function is called with True and False as its arguments, it will return False because the first part of the expression (a and b) returns False and the second part of the expression (not a and not b) returns True. This can also be directly implemented in a Python program as follows:

```
def main():
a = True
b = False
if (a and b) or (not a and not b):
print("The XNOR of", a, "and", b, "is True")
else:
print("The XNOR of", a, "and", b, "is False")
if __name__ == "__main__":
main()
```

## Considerations about logical operators#

The logical operators in Python are used to perform logical operations on boolean values. The and operator returns True if and only if both of its operands are True, the or operator returns True if and only if at least one of its operands is True, and the not operator returns True if and only if its operand is False. The and, or, and not operators can be combined to implement the NAND, NOR, XOR, and XNOR operators.

Other built-in operators like the ^ operator can also be used to implement the XOR operator, and the == operator can be used to implement the XNOR operator. The operator module in Python provides a function called xor that can be used to implement the XOR operator. The logical operators in Python are used to perform logical operations on boolean values, and can be combined to implement the NAND, NOR, XOR, and XNOR operators.