Save a list of functions in Python

I have written the following code in Python where the intent is to make a list of every possible boolean function which takes arguments from the set var_set. So for instance if var_set is {"P","Q"} then all_var_evals(var_set) should contain four functions. One function would return True on input "P" and input "Q", another would return True on input "P" but False on input "Q", and so on.

def all_var_evals(var_set):
    # The bucket is an "accumulator" variable, into which I will place each evaluation as I 
    # construct them.  The bucket will then be returned at the end.
    bucket = []
    var_list = list(var_set) # Gives the variables an indexing (ordering)
    for row in range(2**(len(var_set))): # 2^n evaluations
        to_bin = row 
        func_list = []
        while to_bin != 0:
            func_list.insert(0, to_bin % 2)
            to_bin -= to_bin % 2
            to_bin //= 2
        while len(func_list) < len(var_list):
            func_list.insert(0,0)
        def f():
            return lambda x: func_list[var_list.index(x)]
        bucket.append(f())

    return bucket

However, after testing, I find that every function in the list seems to return True on every input. I assume this is because of some kind of copy issue, like every time func_list takes new values, every function in the bucket now points to it. I tried resolving the copy issue by making a closure, hence why it has

def f():
    return lambda x: func_list[var_list.index(x)]

However, that did not resolve the issue. Since I've never implemented closures in Python, though, I wasn't sure how they work and after reading up on them, I still can't see how to get the desired behavior.

I also tried using .hardcopy() in a few different ways, none of which worked.