# Why does "not(True) in [False, True]" return False?

## Question:

If I do this:

``````>>> False in [False, True]
True
``````

That returns `True`. Simply because `False` is in the list.

But if I do:

``````>>> not(True) in [False, True]
False
``````

That returns `False`. Whereas `not(True)` is equal to `False`:

``````>>> not(True)
False
``````

Why?

Operator precedence. `in` binds more tightly than `not`, so your expression is equivalent to `not((True) in [False, True])`.

It’s all about operator precedence (`in` is stronger than `not`). But it can be easily corrected by adding parentheses at the right place:

``````(not(True)) in [False, True]  # prints true
``````

writing:

``````not(True) in [False, True]
``````

is the same like:

``````not((True) in [False, True])
``````

which looks if `True` is in the list and returns the “not” of the result.

Operator precedence 2.x, 3.x. The precedence of `not` is lower than that of `in`. So it is equivalent to:

``````>>> not ((True) in [False, True])
False
``````

This is what you want:

``````>>> (not True) in [False, True]
True
``````

As @Ben points out: It’s recommended to never write `not(True)`, prefer `not True`. The former makes it look like a function call, while `not` is an operator, not a function.

It is evaluating as `not True in [False, True]`, which returns `False` because `True` is in `[False, True]`

If you try

``````>>>(not(True)) in [False, True]
True
``````

You get the expected result.

`not x in y` is evaluated as `x not in y`

You can see exactly what’s happening by disassembling the code. The first case works as you expect:

``````>>> x = lambda: False in [False, True]
>>> dis.dis(x)
9 BUILD_LIST               2
12 COMPARE_OP               6 (in)
15 RETURN_VALUE
``````

The second case, evaluates to `True not in [False, True]`, which is `False` clearly:

``````>>> x = lambda: not(True) in [False, True]
>>> dis.dis(x)
9 BUILD_LIST               2
12 COMPARE_OP               7 (not in)
15 RETURN_VALUE
>>>
``````

What you wanted to express instead was `(not(True)) in [False, True]`, which as expected is `True`, and you can see why:

``````>>> x = lambda: (not(True)) in [False, True]
>>> dis.dis(x)
3 UNARY_NOT
10 BUILD_LIST               2
13 COMPARE_OP               6 (in)
16 RETURN_VALUE
``````

Let’s see it as a collection containment checking operation: `[False, True]` is a list containing some elements.

The expression `True in [False, True]` returns `True`, as `True` is an element contained in the list.

Therefore, `not True in [False, True]` gives the “boolean opposite”, `not` result of the above expression (without any parentheses to preserve precedence, as `in` has greater precedence than `not` operator).
Therefore, `not True` will result `False`.

On the other hand, `(not True) in [False, True]`, is equal to `False in [False, True]`, which is `True` (`False` is contained in the list).

Alongside the other answers that mentioned the precedence of `not` is lower than `in`, actually your statement is equivalent to :

``````not (True in [False, True])
``````

But note that if you don’t separate your condition from the other ones, python will use 2 roles (`precedence` or `chaining`) in order to separate that, and in this case python used precedence. Also, note that if you want to separate a condition you need to put all the condition in parenthesis not just the object or value :

``````(not True) in [False, True]
``````

But as mentioned, there is another modification by python on operators that is chaining:

Based on python documentation :

Note that comparisons, membership tests, and identity tests, all have the same precedence and have a left-to-right chaining feature as described in the Comparisons section.

For example the result of following statement is `False`:

``````>>> True == False in [False, True]
False
``````

Because python will chain the statements like following :

``````(True == False) and (False in [False, True])
``````

Which exactly is `False and True` that is `False`.

You can assume that the central object will be shared between 2 operations and other objects (False in this case).

And note that its also true for all Comparisons, including membership tests and identity tests operations which are following operands :

``````in, not in, is, is not, <, <=, >, >=, !=, ==
``````

Example :

``````>>> 1 in [1,2] == True
False
``````

Another famous example is number range :

``````7<x<20
``````

which is equal to :

``````7<x and x<20
``````

To clarify on some of the other answers, adding parentheses after a unary operator does not change its precedence. `not(True)` does not make `not` bind more tightly to `True`. It’s just a redundant set of parentheses around `True`. It’s much the same as `(True) in [True, False]`. The parentheses don’t do anything. If you want the binding to be more tight, you have to put the parentheses around the whole expression, meaning both the operator and the operand, i.e., `(not True) in [True, False]`.

To see this another way, consider

``````>>> -2**2
-4
``````

`**` binds more tightly than `-`, which is why you get the negative of two squared, not the square of negative two (which would be positive four).

What if you did want the square of negative two? Obviously, you’d add parentheses:

``````>>> (-2)**2
4
``````

However, it’s not reasonable to expect the following to give `4`

``````>>> -(2)**2
-4
``````

because `-(2)` is the same as `-2`. The parentheses do absolutely nothing. `not(True)` is exactly the same.

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