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S(T) is a monomial. If it is S+T no.
It is the expression t - s
There are much more than three types of scales, but the 3 basic scales are the common major scale (T T S T T T S), the harmonic minor (T S T T S T1/2 S) and the melodic minor (T S T T T T S ascending - T S T T S T T descending). In brackets noticed I labelled the structure of the scale in tones and semitones. T = tone S = semitone T1/2 = minor 3rd/augmented 2nd interval (3 semitones)
T t s t t t s
A mapping, f, from set S to set T is said to be surjective if for every element in set T, there is some element in S such that it maps on to the element in T. Thus, if t is any element of T, there must be some element, s, in S such that f(s) = t.