Question

an animal sanctuary houses a variety of animals. to understand the workload of the sanctuary’s veterinarians, the director looked at which types of animals are treated or not treated by various doctors. the venn diagram shows this information for three of the doctors.
(a) select all the doctors who do not treat birds.
□ dr. chen □ dr. allen □ dr. taylor
(b) how many types of animals are treated by dr. chen or dr. taylor (or both)?
(c) which types of animals are treated by neither dr. chen nor dr. allen nor dr. taylor? choose all that apply.
□ birds □ cats □ dogs □ elks □ frogs
□ goats □ horses □ koalas □ mice □ otters
□ rabbits □ snakes □ turtles

Explanation:

Part (a)

Step1: Analyze Dr. Chen's animals

Dr. Chen's circle has Horses, Dogs, Birds, Cats, Turtles. So he treats birds.

Step2: Analyze Dr. Allen's animals

Dr. Allen's circle has Frogs, Snakes, Otters, Birds, Cats, Rabbits, Elks. So he treats birds.

Step3: Analyze Dr. Taylor's animals

Dr. Taylor's circle has Turtles, Cats, Rabbits, Elks. No birds here. So Dr. Taylor does not treat birds. Wait, wait, no—wait, the Venn: Dr. Chen's circle (left) has Horses, Dogs, and the overlap with Allen (Birds), overlap with Taylor (Turtles), and all three (Cats). Dr. Allen (right) has Frogs, Snakes, Otters, overlap with Chen (Birds), overlap with Taylor (Rabbits), all three (Cats), and Elks? Wait, maybe I misread. Wait, the "Treated by Dr. Chen" circle: Horses, Dogs, and the intersections. "Treated by Dr. Allen": Frogs, Snakes, Otters, and intersections. "Treated by Dr. Taylor": Turtles, and intersections. The animals not in any circle: Mice, Goats, Koalas. Wait, for part (a): doctors who do not treat birds. So check which doctors' circles do not include birds. Dr. Chen's circle includes Birds (in the overlap with Allen). Dr. Allen's circle includes Birds (overlap with Chen). Dr. Taylor's circle: Turtles, Cats (all three), Rabbits (overlap with Allen), Elks (only Taylor? Wait, the Venn: Dr. Taylor's circle (bottom) has Turtles (only Taylor), Cats (all three), Rabbits (Allen and Taylor), Elks (only Taylor). So Dr. Taylor's circle does not have Birds. So Dr. Taylor does not treat birds? Wait, no—wait, the "Treated by Dr. Chen" and "Treated by Dr. Allen" overlap has Birds. So Dr. Chen and Dr. Allen both treat birds (since Birds are in their overlap). Dr. Taylor's circle: does it include Birds? No. So the doctor who does not treat birds is Dr. Taylor? Wait, but let's re-express:

• Dr. Chen: treats Horses, Dogs, Birds (with Allen), Cats (all three), Turtles (with Taylor). So he treats birds.
• Dr. Allen: treats Frogs, Snakes, Otters, Birds (with Chen), Cats (all three), Rabbits (with Taylor), Elks (only Allen? Wait, Elks is in Taylor's circle? Wait, the "Treated by Dr. Taylor" circle has Elks? Wait, the diagram: "Treated by Dr. Taylor" circle (bottom) has Turtles (only Taylor), Cats (all three), Rabbits (Allen and Taylor), Elks (only Taylor? Or Allen and Taylor? Wait, maybe the Elks is in Taylor's circle. So Dr. Allen's circle: Frogs, Snakes, Otters, Birds (Chen), Cats (all), Rabbits (Taylor), Elks (Taylor)? No, maybe I messed up. Alternatively, maybe the correct approach: Birds are in the intersection of Chen and Allen (only Chen and Allen, not Taylor). So Dr. Chen treats birds (because Birds are in his circle's overlap), Dr. Allen treats birds (same), Dr. Taylor's circle does not include Birds (since Birds are only in Chen-Allen overlap). So Dr. Taylor does not treat birds. Wait, but the options are Dr. Chen, Dr. Allen, Dr. Taylor. So the doctor who does not treat birds is Dr. Taylor? Wait, no—wait, maybe I made a mistake. Wait, let's check again. The Venn diagram:

• Left circle (Dr. Chen): Horses, Dogs, and the two-way overlaps (with Allen: Birds; with Taylor: Turtles) and three-way (Cats).
• Right circle (Dr. Allen): Frogs, Snakes, Otters, two-way overlaps (with Chen: Birds; with Taylor: Rabbits) and three-way (Cats), and maybe Elks?
• Bottom circle (Dr. Taylor): Turtles (two-way with Chen), Cats (three-way), Rabbits (two-way with Allen), Elks (only Taylor).

So Birds are only in the overlap of Chen and Allen (not Taylor). So Dr. Chen treats birds (because Birds are in his circle's region), Dr. Allen treats birds (same), Dr. Taylor's circle does no…

Step1: List animals treated by Dr. Chen or Dr. Taylor (or both). "Or both" means union of Dr. Chen's set and Dr. Taylor's set.

Dr. Chen's set (all animals in his circle or overlaps): Horses, Dogs, Birds (Chen∩Allen), Turtles (Chen∩Taylor), Cats (all three).

Dr. Taylor's set (all animals in his circle or overlaps): Turtles (Chen∩Taylor), Cats (all three), Rabbits (Allen∩Taylor), Elks (only Taylor).

Now, union of these two sets: combine all unique animals from both.

Dr. Chen's animals: Horses, Dogs, Birds, Turtles, Cats.

Dr. Taylor's animals: Turtles, Cats, Rabbits, Elks.

Union: Horses, Dogs, Birds, Turtles, Cats, Rabbits, Elks.

Now count them: Horses (1), Dogs (1), Birds (1), Turtles (1), Cats (1), Rabbits (1), Elks (1). Wait, that's 7? Wait, no—wait, let's list each:

• Only Dr. Chen: Horses, Dogs (2)
• Chen∩Allen: Birds (1)
• Chen∩Taylor: Turtles (1)
• All three: Cats (1)
• Allen∩Taylor: Rabbits (1)
• Only Dr. Taylor: Elks (1)

Wait, that's 2 + 1 + 1 + 1 + 1 + 1 = 7? Wait, no: Horses (only Chen), Dogs (only Chen), Birds (Chen&Allen), Turtles (Chen&Taylor), Cats (all), Rabbits (Allen&Taylor), Elks (only Taylor). So that's 7 animals. Wait, but let's check again. Dr. Chen's set: Horses, Dogs, Birds, Turtles, Cats. Dr. Taylor's set: Turtles, Cats, Rabbits, Elks. The union is Horses, Dogs, Birds, Turtles, Cats, Rabbits, Elks. That's 7 animals. So the number is 7.

Part (c)

Animals treated by neither Dr. Chen nor Dr. Allen nor Dr. Taylor are the ones outside all three circles. From the diagram, those are Mice, Goats, Koalas. So we select Mice, Goats, Koalas.

Final Answers:

(a) Dr. Taylor (the checkbox for Dr. Taylor should be selected)

(b) 7

(c) Mice, Goats, Koalas (select those checkboxes)

But since the user might want each part's answer:

(a) # Brief Explanations:
Check which doctors’ treated animals (Venn circles) do not include birds. Dr. Chen and Dr. Allen’s circles include birds (in their overlap), while Dr. Taylor’s circle does not.

Answer:

Dr. Taylor (select the checkbox for Dr. Taylor)

(b) # Explanation:

Step1: Identify animals in Dr. Chen’s set: Horses, Dogs, Birds, Turtles, Cats.

Step2: Identify animals in Dr. Taylor’s set: Turtles, Cats, Rabbits, Elks.

Step3: Find the union (animals in either set): Horses, Dogs, Birds, Turtles, Cats, Rabbits, Elks. Count: 7.