Final answer:
Sets A (b, b, b, b, b, c, c, c, a, a) and C (a, a, b, b, c, c) are equal to the set (a, b, c) because the repetition of elements in sets does not matter, while sets B and D are not equal due to the presence of extra elements not in the set (a, b, c).
Step-by-step explanation:
To determine which sets are equal to the set (a, b, c), we need to consider the properties of sets in mathematics. A set is a collection of unique elements, and the order in which they are listed does not matter. Thus, a set with the elements a, b, and c is equal to any other set that contains these three elements and only these three, regardless of the order or repetition of the elements.
Therefore, looking at the sets provided:
- Set A: (b, b, b, b, b, c, c, c, a, a) contains the elements a, b, and c with repetition, but since sets do not care about repetition, Set A is equal to the set (a, b, c).
- Set B: {a, a, b, b, c, x} contains an extra element 'x' that is not in the set (a, b, c), so Set B is not equal.
- Set C: (a, a, b, b, c, c) contains the elements a, b, and c with repetition, which, as mentioned, does not affect the equality, so Set C is equal to the set (a, b, c).
- Set D: (b, b, b, x, x, x, c, c) not only contains repetition but also includes element 'x' which is not in the set (a, b, c), so Set D is not equal.
In conclusion, sets A and C are equal to the set (a, b, c).