from typing import List
from typing import Tuple


def check_intervals(intervals: List[Tuple[int, int]]) -> bool:
    """
    Check intervals to make sure that they are sorted and non-intersecting.
    :param intervals: a list of intervals, represented as tuples (a,b)
    :return: True if the list is non-overlapping, and false otherwise.
    """
    for (interval1, interval2) in zip(intervals, intervals[1:]):
        if interval1[1] >= interval2[0]:
            return False
    return True