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Establish which of the following statements are true. (a) a sequence is convergent if and only if all of its subsequences are convergent. (b) a sequence is bounded if and only if all of its subsequences are bounded. (c) a sequence is monotonic if and only if all of its subsequences are monotonic.

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Assume that there is a 4% rate of disk drive failure in a year. a. if all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. if copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?