.The construction of the circle of fifths is based on a simple grade 4 operation: skip counting. In particular, we skip count by 7 semitones. By skip counting by 7 semitones, we will produce the entire chromatic scale (always, staying inside one octave). This is modular arithmetic on Z12: let us do some calculations in Z12 applied to music. (a) Let a = 2 Z12. Get all the values constructed by the sequence a + 7n, where n = 0, 1, 2, .... get the result using only numbers between 0 and 11. (b) Let a = 2 Z12 again. Get all the values constructed by the sequence a + 5n, where n = 0, 1, 2, .... Get the result using only numbers between 0 and 11. (c) Let a = 2 Z12 again. Get all the values constructed by the sequence a + 4n, where n = 0, 1, 2, .... Write the result using only numbers between 0 and 11. (d) Using the previous three examples, get a general rule that determines all the skip counting sequences that generate the entire group Z12