Final answer:
A sequence is considered bounded if its terms are limited by some constant value. However, the boundedness of a sequence and its subsequences are not necessarily related.
Step-by-step explanation:
A sequence is considered bounded if its terms are limited by some constant value. Conversely, a subsequence is a sequence that is derived from a given sequence by deleting some elements without changing their order.
In general, the boundedness of a sequence and its subsequences are not necessarily related. There can be instances where a sequence is bounded, but some of its subsequences are unbounded and vice versa. Therefore, the statement 'A sequence is bounded if and only if all of its subsequences are bounded' is False.