Final answer:
The correct representation of Set Q containing the unique letters from the word SISTER is Set Q = {S, I, T, E, R}. This set includes all distinct letters presented once, as per set theory rules.
Step-by-step explanation:
The question involves determining which set contains all the unique letters in the word SISTER. When we examine the word SISTER, we see that it consists of six letters. However, there is a repetition of the letter S. In set theory, a set is a collection of distinct objects, considered as an object in its own right. This means that each unique element appears only once, and any repetitions are ignored.
Set Q must therefore include every letter from SISTER without any repetitions. Considering the provided options, Set Q = {S, I, T, E, R} is the correct answer because it contains all the distinct letters from the word SISTER, with each letter listed only once.
Option A: Q = { I, E } includes only two letters from the word and is thus incomplete.
Option B: Q = { S, T, R } is also incomplete as it does not include the letters I and E from the word SISTER.
Option C: Q = { S, I, S, T, E, R } is incorrect because it lists the letter S twice, which violates the definition of a set where each element must be unique.
The final Option D: Q = { S, I, T, E, R } correctly lists all unique letters from the word SISTER exactly once, making it the correct representation of Set Q.