1. Write out the elements of the following sets
2. Let Σ := {A, B, . . . , Z} denote the English alphabet. Using notation from this chapter, give an expression that denotes each of the following sets. It may be useful to recall that Σ k denotes the set of strings consisting of a sequence of k elements from Σ, so Σ 0 contains the unique string of length 0 (called the empty string, and typically denoted by ε—or by "" in most programming languages).
1. The set of 8-letter strings.
2. The set of 5-letter strings that do not contain any vowels {A, E, I, O, U}.
3. The set of 6-letter strings that do not contain more than one vowel. (So GRITTY, QWERTY, and
BRRRRR are fine; but EEEEEE, THREAT, STRENGTHS, and A are not.)