In a proof like this (checking if a set is included into another) you typically take one arbitrary element x from the first set, and prove that it also belongs to the second set. (So any element from the first is included in the second, so the first set is a subset of the second.)
If x is in the first set, then it is either in A or in B (or both), but certainly not in C. Try to figure out each of the two cases (x in A, x in B), and see if, in both cases, x belongs to the second set.
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