Comparing two lists for same value

Let’s say I have 3 lists:

a = [0,0,0,1,1]
b = [1,0,0,0,0]
c = [1,1,1,0,0]

I want to return False whenever there are 1’s at the same position, so for ‘b & c’ it would return False, because they both have a one at index 0, ‘a & b’ and ‘a & c’ should return True in this case.

The way I would do it is:

for i in range(0, len(a)):
   if a[i] == 1 and b[i] == 1:
      return False
return True

Though I feel this is very inefficient. Is there an easier and more efficient way to do this? I was thinking of using binary AND, but not sure how to implement that.

>>> a = [0,0,0,1,1]
>>> b = [1,0,0,0,0]
>>> c = [1,1,1,0,0]
>>> def f(a,b):
...   return all([False if a[i] == 1 and b[i] == 1 else True for i in range(0, len(a))])
...
>>> print(f(a,b), f(b,c), f(a,c))
True False True