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Math  /  Discrete

QuestionLet U=\mathrm{U}= \{people at Mount College },A={\}, A=\{ students at Mount College }\}, B={B=\{ teachers at Mount College },C={\}, C=\{ live on campus at Mount College }\}, and D={D=\{ live off campus at Mount College }\}. Describe verbally the set. D′D^{\prime}
Choose the correct answer below. A. \{live on campus at Mount College \} B. \{live off campus at Mount College \} C. \{not teachers at Mount College \} D. \{teachers at Mount College }\}

Studdy Solution

STEP 1

1. The universal set U\mathrm{U} includes all people at Mount College.
2. Set DD includes individuals who live off campus at Mount College.
3. The complement of a set, denoted by D′D^{\prime}, includes all elements in the universal set U\mathrm{U} that are not in set DD.

STEP 2

1. Understand the concept of set complement.
2. Identify the elements in the complement D′D^{\prime}.
3. Match the description of D′D^{\prime} with the given options.

STEP 3

Understand the concept of set complement: - The complement of a set DD, denoted D′D^{\prime}, consists of all elements in the universal set U\mathrm{U} that are not in DD.

STEP 4

Identify the elements in the complement D′D^{\prime}: - Since DD is the set of people who live off campus at Mount College, D′D^{\prime} will include all people at Mount College who do not live off campus.

STEP 5

Match the description of D′D^{\prime} with the given options: - D′D^{\prime} includes those who do not live off campus, which means they live on campus. - Therefore, the correct description of D′D^{\prime} is: \{live on campus at Mount College\}.
The correct answer is: A. \{live on campus at Mount College\}.

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