Representation of Sets and Repeated Elements

The governing property is that a set records membership, not the number of times an element is written. Repeated occurrences of the same value do not create additional elements. In O, the distinct values are 7, 8, and 9. Removing the repeated writing gives the equivalent roster form O = {7, 8, 9}, so option A is correct. Option B still contains a repeated 7 and is not the simplified representation expected here. Option C omits 9, and option D retains only 9 while omitting 7 and 8. Thus equality of sets depends on having exactly the same distinct elements, not on matching the number of written entries or their repetitions.

The governing property is that a set contains distinct elements only; repeated appearances do not increase its cardinality. Although eight entries are written in the display, the only different values are 1, 2, and 3. We can simplify the set to Z = {1, 2, 3}, so n(Z) = 3. Option C counts every written occurrence and treats the set like a list or multiset. Options B and D do not equal the number of distinct values either. The three copies of 1, two copies of 2, and three copies of 3 still represent only three set members. Therefore option A is correct.