# Partitions of a Set

Prove that if a partition g is finer than a partition f, then any union of sets of f is a union of sets of g.

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Set Partitions and Bit Strings

Which of these collections of subsets are partitions on the set of bit strings of length 8?

a) The set of bit strings that end with 00; the set of bit strings that end with 01; the set of bit strings that end with 10; and the set of bit strings that end with 11.

b) The set of bit strings that end with 111; the set of bit strings that end with 011; and the set of bit strings that end with 00.

c) The set of bit strings that have 3k ones, where k is a non-negative integer; the set of bit strings that contain 3k+1 ones, where k is a non-negative integer; and the set of bit strings that contain 3k+2 ones, where k is a non-negative integer.

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