Final answer:
To express the set of children older than 7 using roster notation, we need the Venn diagram. Roster notation involves listing all elements in a set within braces. Without the actual Venn diagram, the correct set can't be determined.
Step-by-step explanation:
To determine the set of children older than 7 using roster notation from the information provided, we need the specifics from the Venn diagram which are not given in the question. However, assuming that there is enough information in the Venn diagram to make this determination, roster notation would simply list the names of the children who are older than 7 within braces ({}).
If, for instance, the Venn diagram indicated that Ben, Max, Kyle, Ayesha, and Kate are the only children older than 7, then we would write the set as {Ben, Max, Kyle, Ayesha, Kate}. Without the actual diagram, we cannot definitively choose the correct option from A to D. However, the roster notation itself is a method of specifying a set in which all the elements of the set are listed out, and it is particularly useful in organizing and presenting information in a clear and concise manner.