Use Venn diagrams to check the validity of the argument

All cats are animals.
This is not an animal.
Therefore, this is not a cat.

To use Venn diagrams to check the validity of the argument, we will create two circles: one representing "cats" and the other representing "animals."

In a Venn diagram, we usually represent categories or sets as circles, and the overlapping area represents the elements that belong to both categories.

1. Start by drawing a large circle to represent "animals" and label it accordingly.
2. Draw another circle inside the "animals" circle to represent "cats" and label it accordingly.
3. According to the first premise, "All cats are animals," so make sure that the circle representing "cats" is completely inside the circle representing "animals."
4. Now, consider the second premise, which states, "This is not an animal." Since "this" is not part of the circle representing "animals," it must be outside that circle.
5. Next, based on the conclusion, "Therefore, this is not a cat," we need to determine if "this" is also outside the circle representing "cats."
6. If "this" is outside the circle representing "cats" but still within the circle representing "animals," then the argument is valid. This is because if "this" is not a cat, it can still be an animal.
7. However, if "this" is outside both circles, meaning it lies in the region that is not part of either "cats" or "animals," then the argument is invalid. This is because if "this" is not an animal, it cannot be considered a cat.

By visually inspecting the Venn diagram, we can determine if the argument is valid or invalid based on the positions of the relevant elements.