Math / Discrete

QuestionLast week, there were several types of animals at a local animal shelter. Let $U$ be the set of the types of animals at the shelter last week. During the week, some of the animals were treated by the veterinarians on staff. Let $B$ . be the set of animal types that were treated by Dr. Brown. Let $D$ be the set of animal types that were treated by Dr. Dean. Let $N$ be the set of animal types that were treated by Dr. Nelson. Use the Venn diagram to get your answers below.
Consider this set (which is written in descriptive form): The set of animal types that were not treated by Dr. Nelson, but were treated by Dr. Brown or Dr. Dean (a) Which of these is a correct way to write the set? $N^{\prime} \cap(B \cup D)$ $N^{\prime} \cup(B \cup D)$ $N^{\prime} \cap(B \cap D)$ $N^{\prime} \cup(B \cap D)$ (b) Write the set in roster form. $\square$ , $\ldots$ birds cats dogs ferrets gerbils snakes mice pigs rabbits

Studdy Solution

STEP 1

1. The set of animal types at the shelter last week is denoted by $U$ .
2. $B$ is the set of animal types treated by Dr. Brown.
3. $D$ is the set of animal types treated by Dr. Dean.
4. $N$ is the set of animal types treated by Dr. Nelson.
5. We need to determine the correct set notation for the animal types not treated by Dr. Nelson but treated by Dr. Brown or Dr. Dean.
6. We need to write this set in roster form based on the given Venn diagram.

STEP 2

1. Identify the correct set notation for the set of animal types not treated by Dr. Nelson but treated by Dr. Brown or Dr. Dean.
2. Write the set in roster form using the given animal types and the Venn diagram.

STEP 3

Identify the correct set notation for the animal types that were not treated by Dr. Nelson ( $N^{\prime}$ ) but were treated by Dr. Brown ( $B$ ) or Dr. Dean ( $D$ ).
$N^{\prime} \cap (B \cup D)$
This notation represents the set of animal types that are not in $N$ but are in the union of $B$ and $D$ .

STEP 4

Write the set $N^{\prime} \cap (B \cup D)$ in roster form by examining the Venn diagram.
From the Venn diagram, we identify the animal types in $(B \cup D)$ that are not in $N$ : - Animals in $B$ only: Dogs, Cats, Turtles - Animals in $D$ only: Rabbits - Animals in both $B$ and $D$ but not in $N$ : Ferrets
Thus, the set in roster form is:
$\{ \text{Dogs, Cats, Turtles, Rabbits, Ferrets} \}$
Therefore, the correct way to write the set is $N^{\prime} \cap (B \cup D)$ , and the set in roster form is $\{\text{Dogs, Cats, Turtles, Rabbits, Ferrets}\}$ .

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