Perceptrons: Functions not learnable without bias

Question

I am trying to determine which functions are not learnable without a bias when building a perceptron. The set of functions I need to evaluate is {NOT, OR, AND}.

Could someone help interpret these results?

AND FUNCTION

https://imgur.com/a/OTFUT

OR FUNCTION

I get a divide by 0 error in my script.

NOT FUNCTION

https://imgur.com/a/wZnxT

It would appear that the AND function does not crash like the OR function but the end result is incorrect. The OR function simply won't graph due to a divide by 0 error. The NOT function appears to still be learnable.

If desired, I can post my python script with how I generated these graphs. I am using a sigmoid activate function.