How do you get the logical xor of two variables in Python?

If you're already normalizing the inputs to booleans, then != is xor.

bool(a) != bool(b)

You can always use the definition of xor to compute it from other logical operations:

(a and not b) or (not a and b)

But this is a little too verbose for me, and isn't particularly clear at first glance. Another way to do it is:

bool(a) ^ bool(b)

The xor operator on two booleans is logical xor (unlike on ints, where it's bitwise). Which makes sense, since bool is just a subclass of int, but is implemented to only have the values 0 and 1. And logical xor is equivalent to bitwise xor when the domain is restricted to 0 and 1.

So the logical_xor function would be implemented like:

def logical_xor(str1, str2):
    return bool(str1) ^ bool(str2)

Credit to Nick Coghlan on the Python-3000 mailing list.

As Zach explained, you can use:

xor = bool(a) ^ bool(b)

Personally, I favor a slightly different dialect:

xor = bool(a) + bool(b) == 1

This dialect is inspired from a logical diagramming language I learned in school where "OR" was denoted by a box containing ≥1 (greater than or equal to 1) and "XOR" was denoted by a box containing =1.

This has the advantage of correctly implementing exclusive or on multiple operands.

• "1 = a ^ b ^ c..." means the number of true operands is odd. This operator is "parity".
• "1 = a + b + c..." means exactly one operand is true. This is "exclusive or", meaning "one to the exclusion of the others".

• Python logical or: A or B: returns A if bool(A) is True, otherwise returns B
• Python logical and: A and B: returns A if bool(A) is False, otherwise returns B

To keep most of that way of thinking, my logical xor definintion would be:

def logical_xor(a, b):
    if bool(a) == bool(b):
        return False
    else:
        return a or b

That way it can return a, b, or False:

>>> logical_xor('this', 'that')
False
>>> logical_xor('', '')
False
>>> logical_xor('this', '')
'this'
>>> logical_xor('', 'that')
'that'

Python has a bitwise exclusive-OR operator, it's ^:

>>> True ^ False
True
>>> True ^ True
False
>>> False ^ True
True
>>> False ^ False
False

You can use it by converting the inputs to booleans before applying xor (^):

bool(a) ^ bool(b)

(Edited - thanks Arel)

To get the logical xor of two or more variables in Python:

1. Convert inputs to booleans
2. Use the bitwise xor operator (^ or operator.xor)

For example,

bool(a) ^ bool(b)

When you convert the inputs to booleans, bitwise xor becomes logical xor.

Note that the accepted answer is wrong: != is not the same as xor in Python because of the subtlety of operator chaining.

For instance, the xor of the three values below is wrong when using !=:

True ^  False ^  False  # True, as expected of XOR
True != False != False  # False! Equivalent to `(True != False) and (False != False)`

(P.S. I tried editing the accepted answer to include this warning, but my change was rejected.)

Given that A and B are bools.

A is not B

You use the same XOR operator like in C, which is ^.

I don't know why, but the most upvoted solution suggests bool(A) != bool(B), while I would say - in conformity with C's ^'s operator, the most obvious solution is:

bool(A) ^ bool(B)

which is more readable and immediately understandable for anyone coming from C or any C-derived language ...

when doing code-golfing, probably

not A ^ (not B)

will be the winner. with not as converter for boolean (one letter less than bool(). And for the first expression in some cases one can leave out the parantheses. Well, it depends, in cases where one has to do not(A) ^ (not(B)), the bool() needs same amount of letters ...

Exclusive Or is defined as follows

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

Some of the implementations suggested here will cause repeated evaluation of the operands in some cases, which may lead to unintended side effects and therefore must be avoided.

That said, a xor implementation that returns either True or False is fairly simple; one that returns one of the operands, if possible, is much trickier, because no consensus exists as to which operand should be the chosen one, especially when there are more than two operands. For instance, should xor(None, -1, [], True) return None, [] or False? I bet each answer appears to some people as the most intuitive one.

For either the True- or the False-result, there are as many as five possible choices: return first operand (if it matches end result in value, else boolean), return first match (if at least one exists, else boolean), return last operand (if ... else ...), return last match (if ... else ...), or always return boolean. Altogether, that's 5 ** 2 = 25 flavors of xor.

def xor(*operands, falsechoice = -2, truechoice = -2):
  """A single-evaluation, multi-operand, full-choice xor implementation
  falsechoice, truechoice: 0 = always bool, +/-1 = first/last operand, +/-2 = first/last match"""
  if not operands:
    raise TypeError('at least one operand expected')
  choices = [falsechoice, truechoice]
  matches = {}
  result = False
  first = True
  value = choice = None
  # avoid using index or slice since operands may be an infinite iterator
  for operand in operands:
    # evaluate each operand once only so as to avoid unintended side effects
    value = bool(operand)
    # the actual xor operation
    result ^= value
    # choice for the current operand, which may or may not match end result
    choice = choices[value]
    # if choice is last match;
    # or last operand and the current operand, in case it is last, matches result;
    # or first operand and the current operand is indeed first;
    # or first match and there hasn't been a match so far
    if choice < -1 or (choice == -1 and value == result) or (choice == 1 and first) or (choice > 1 and value not in matches):
      # store the current operand
      matches[value] = operand
    # next operand will no longer be first
    first = False
  # if choice for result is last operand, but they mismatch
  if (choices[result] == -1) and (result != value):
    return result
  else:
    # return the stored matching operand, if existing, else result as bool
    return matches.get(result, result)

testcases = [
  (-1, None, True, {None: None}, [], 'a'),
  (None, -1, {None: None}, 'a', []),
  (None, -1, True, {None: None}, 'a', []),
  (-1, None, {None: None}, [], 'a')]
choices = {-2: 'last match', -1: 'last operand', 0: 'always bool', 1: 'first operand', 2: 'first match'}
for c in testcases:
  print(c)
  for f in sorted(choices.keys()):
    for t in sorted(choices.keys()):
      x = xor(*c, falsechoice = f, truechoice = t)
      print('f: %d (%s)\tt: %d (%s)\tx: %s' % (f, choices[f], t, choices[t], x))
  print()

Many folks, including myself, need an xor function that behaves like an n-input xor circuit, where n is variable. (See https://en.wikipedia.org/wiki/XOR_gate). The following simple function implements this.

def xor(*args):
   """
   This function accepts an arbitrary number of input arguments, returning True
   if and only if bool() evaluates to True for an odd number of the input arguments.
   """

   return bool(sum(map(bool,args)) % 2)

Sample I/O follows:

In [1]: xor(False, True)
Out[1]: True

In [2]: xor(True, True)
Out[2]: False

In [3]: xor(True, True, True)
Out[3]: True

How about this?

(not b and a) or (not a and b)

will give a if b is false
will give b if a is false
will give False otherwise

Or with the Python 2.5+ ternary expression:

(False if a else b) if b else a

Xor is ^ in Python. It returns :

• A bitwise xor for ints
• Logical xor for bools
• An exclusive union for sets
• User-defined results for classes that implements __xor__.
• TypeError for undefined types, such as strings or dictionaries.

If you intend to use them on strings anyway, casting them in bool makes your operation unambiguous (you could also mean set(str1) ^ set(str2)).

This is how I would code up any truth table. For xor in particular we have:

| a | b  | xor   |             |
|---|----|-------|-------------|
| T | T  | F     |             |
| T | F  | T     | a and not b |
| F | T  | T     | not a and b |
| F | F  | F     |             |

Just look at the T values in the answer column and string together all true cases with logical or. So, this truth table may be produced in case 2 or 3. Hence,

xor = lambda a, b: (a and not b) or (not a and b)

It's easy when you know what XOR does:

def logical_xor(a, b):
    return (a and not b) or (not a and b)

test_data = [
  [False, False],
  [False, True],
  [True, False],
  [True, True],
]

for a, b in test_data:
    print '%r xor %s = %r' % (a, b, logical_xor(a, b))

Just because I haven't seen it mentioned elsewhere, this also does the trick:

def logical_xor(a, b):
    return not b if a else bool(b)

I'm not sure if it's "better"/more readable/more pythonic than the accepted solution bool(a) != bool(b).

The way that Python handles logic operations can be confusing, so my implementation gives the user the option (by default) of a simple True/False answer. The actual Python result can be obtained by setting the optional third arg to None.

def xor(a, b, true=True, false=False): # set true to None to get actual Python result
    ab1 = a and not b
    ab2 = not a and b
    if bool(ab1) != bool(ab2):
        return (ab1 or ab2) if true is None else true
    else:
        return false

Here's a generalization.

def xor(*orands):
    return sum(bool(x) for x in orands) == 1

You can test it with

# test
from itertools import product
for a, b, c in product((False, True), repeat=3):
    print(f'{int(a)}{int(b)}{int(c)}|{xor(a,b,c)}')

Output:

000|False
001|True
010|True
011|False
100|True
101|False
110|False
111|False

We can easily find xor of two variables by the using:

def xor(a,b):
    return a !=b

Example:

xor(True,False) >>> True