import typing as t


def chi(multi_set: list[str], other_multi_set: list[str], match_function: t.Callable) -> bool:
    assert len(multi_set) == len(other_multi_set), "Wrong input match lengths!"
    for item in multi_set:
        for other_item in other_multi_set:
            if match_function(item, other_item):
                return True
    return False


def mu(multi_set: list[str], other_multi_set: list[str], match_function: t.Callable) -> int:
    assert len(multi_set) == len(other_multi_set), "Wrong input match lengths!"
    count_intersections = 0
    for item in multi_set:
        for other_item in other_multi_set:
            if match_function(item, other_item):
                count_intersections += 1
    return count_intersections