You have to prove it rigorously. If you know how to do it, then no problem.

If there exists a poly in the intersection, then both the even co-effs and the odd co-effs are 0. But this means all the co-effs are 0. Hence we are doneHowever,?does the intersection of W1 and W2 = 0

If not, then how can I form an example showing this?

If so, how can I prove it?

Please help me understand this!