Questions: Question 22 of 22 (1 point) I Question Attempt: 1 of Unlimited A certain animal shelter has several animal types. We'll call the set of these animal types U. Two veterinarians treated certain animal types yesterday. Let M be the set of animal types treated by Dr. Morgan. Let G be the set of animal types treated by Dr. Gray. Use the Venn diagram to write the descriptive and roster forms of the sets below (a) Set: M ∩ G - Descriptive form: (Choose one) - Roster form: (b) Set: (G ∩ M)′ - Descriptive form: (Choose one)

Question 22 of 22 (1 point) I Question Attempt: 1 of Unlimited

A certain animal shelter has several animal types. We'll call the set of these animal types U. Two veterinarians treated certain animal types yesterday. Let M be the set of animal types treated by Dr. Morgan. Let G be the set of animal types treated by Dr. Gray. Use the Venn diagram to write the descriptive and roster forms of the sets below
(a) Set: M ∩ G
- Descriptive form: (Choose one)
- Roster form:
(b) Set: (G ∩ M)′
- Descriptive form: (Choose one)

Transcript text: Question 22 of 22 (1 point) I Question Attempt: 1 of Unlimited A certain animal shelter has several animal types. We'll call the set of these animal types $U$. Two veterinarians treated certain animal types yesterday. Let $M$ be the set of animal types treated by Dr. Morgan. Let $G$ be the set of animal types treated by Dr. Gray. Use the Venn diagram to write the descriptive and roster forms of the sets bel (a) Set: $M \cap G$ - Descriptive form: $\square$ (Choose one) - Roster form: $\square$ (b) Set: $(G \cap M)^{\prime}$ - Descriptive form: $\square$ (Choose one)

Solution

Solution Steps

Step 1: Identify the sets M and G

Set M (animals treated by Dr. Morgan): snakes, birds, mice
Set G (animals treated by Dr. Gray): birds, mice, turtles, dogs, gerbils

Step 2: Find the intersection of sets M and G

The intersection $ M \cap G $ includes animals treated by both Dr. Morgan and Dr. Gray.
Intersection: birds, mice

Step 3: Write the descriptive and roster forms for $ M \cap G $

Descriptive form: The set of animals treated by both Dr. Morgan and Dr. Gray.
Roster form: {birds, mice}

Step 4: Find the complement of the intersection $ (G \cap M)' $

The complement $ (G \cap M)' $ includes all animals in the universal set $ U $ that are not in the intersection $ M \cap G $.
Universal set $ U $: cats, fish, rabbits, snakes, birds, mice, turtles, dogs, gerbils
Complement: cats, fish, rabbits, snakes, turtles, dogs, gerbils

Step 5: Write the descriptive and roster forms for $ (G \cap M)' $

Descriptive form: The set of animals not treated by both Dr. Morgan and Dr. Gray.
Roster form: {cats, fish, rabbits, snakes, turtles, dogs, gerbils}

Final Answer

(a) Set: $ M \cap G $

Descriptive form: The set of animals treated by both Dr. Morgan and Dr. Gray.
Roster form: {birds, mice}

(b) Set: $ (G \cap M)' $

Descriptive form: The set of animals not treated by both Dr. Morgan and Dr. Gray.
Roster form: {cats, fish, rabbits, snakes, turtles, dogs, gerbils}

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