All zebras are striped animals. no zebra are polar bears. Therefore no polar bears are striped animals?

No.

You have no statement here that shuts polar bears out of the striped animals category. You've put zebras into the striped animals group, but there could be other things in the same group.

You'd have to do that the other way around:

All striped animals are zebras.

No polar bears are striped animals.

Therefore no polar bears are zebras.