Venn Diagram Logic Explained

This question asks us to find the correct Venn diagram that represents the relationship between the sets: Dog, Animal, and Pet.

Understanding the Relationships

To create the correct Venn diagram, we need to understand how these terms relate to each other:

• Animal: This is a very broad category that includes all living creatures that are not plants or other organisms.
• Dog: A dog is a specific type of animal. Therefore, the set 'Dog' is entirely contained within the set 'Animal'. In a Venn diagram, this means the circle representing 'Dog' must be completely inside the circle representing 'Animal'.
• Pet: A pet is an animal kept for pleasure or companionship. This means:
  • Some dogs are pets.
  • Not all dogs are pets (e.g., wild dogs, stray dogs).
  • Some pets are dogs.
  • Some pets are not dogs (e.g., cats, birds, fish).
  This relationship indicates that the set 'Pet' overlaps with the set 'Dog', but neither contains the other completely. The 'Pet' set also contains elements that are not dogs, and the 'Animal' set contains elements that are neither dogs nor pets.

Choosing the Correct Venn Diagram

Based on the relationships identified:

• The 'Dog' set must be a subset of the 'Animal' set.
• The 'Pet' set must intersect with the 'Dog' set (because some dogs are pets).
• The 'Pet' set must also intersect with the 'Animal' set, but potentially in areas outside of 'Dog' (because some pets are not dogs).
• The 'Animal' set contains things that are neither dogs nor pets.

Let's analyze the options based on this logic:

• Diagram 1 (Separate circles): Incorrect, as Dogs are Animals.
• Diagram 2 (One circle inside another, third separate): Incorrect, as Dogs can be Pets.
• Diagram 3: This diagram shows the 'Dog' circle completely inside the 'Animal' circle. The 'Pet' circle overlaps with the 'Dog' circle and also extends into the 'Animal' circle area that is outside 'Dog'. This correctly represents that all dogs are animals, some dogs are pets, and some pets are not dogs.
• Diagram 4 (Three overlapping circles, but Dog not fully inside Animal): Incorrect.

Therefore, the Venn diagram where the 'Dog' circle is fully inside the 'Animal' circle, and the 'Pet' circle overlaps with both, is the correct representation.

Conclusion

The correct Venn diagram representing the relationship between Dog, Animal, and Pet is the one where 'Dog' is a subset of 'Animal', and 'Pet' overlaps with 'Dog' and potentially other parts of 'Animal'. This corresponds to option 3.