Set-Builder Form and Representation of Sets

The governing concept is expressing a roster-form set through a defining property together with suitable bounds. Every element of C is a multiple of 3. Among numbers satisfying 0 ≤ x < 10, the multiples of 3 are exactly 0, 3, 6, and 9. Thus option A produces precisely the given set: the lower bound includes 0, while the strict upper bound excludes 10 and larger values. Option B gives the factors of 9, namely {1, 3, 9}, so it includes 1 and omits 0 and 6. Option C gives odd digits such as 1, 3, 5, 7, and 9. Option D gives prime digits such as 2, 3, 5, and 7; neither matches C.

The governing concept is set-builder representation: one common property must generate every listed member and no extra member. The numbers 0, 1, 4, and 9 are 0², 1², 2², and 3², respectively, and they are precisely the perfect squares less than 10. Thus option A describes exactly C. Option B gives the primes below 10, namely 2, 3, 5, and 7. Option C gives even numbers below 10, while option D gives the factors of 10, namely 1, 2, 5, and 10. A correct set-builder description must match both inclusion and exclusion, so merely sharing some members is insufficient. Therefore A is the only correct option.