Given the argument and its Euler diagram below, determine whether the syllogism is valid or invalid.
All roads come to an end.
Carrollton Avenue is a road.
Carrollton Avenue comes to an end.
I'm assuming that this is your Euler diagram:
Carrollton Ave is part of the set of all roads.
If it is a road, then it must come to an end.
Here is a similar example.
All parallelograms are quadrilaterals.
Squares are parallelograms.
You can conclude that squares are quadrilaterals.
Valid
To determine the validity of the syllogism, we can use the Euler diagram given. An Euler diagram is a visual representation of the premises and conclusions of a syllogism using circles or ovals to represent categories or classes.
Let's represent the given statements in the Euler diagram:
1. All roads come to an end.
We can represent this statement by drawing a circle labeled "Roads" and shading the area that represents "coming to an end."
2. Carrollton Avenue is a road.
Next, we draw another circle labeled "Carrollton Avenue" inside the "Roads" circle.
The resulting Euler diagram shows that Carrollton Avenue is indeed within the category of roads and therefore satisfies the second premise.
3. Carrollton Avenue comes to an end.
Based on the diagram, we can observe that Carrollton Avenue falls within the shaded region of the "Roads" circle representing "coming to an end." Therefore, the conclusion is also true, as Carrollton Avenue does, in fact, come to an end.
Since both premises are true and the conclusion follows logically from them, we can conclude that the syllogism is valid.
Note: The Euler diagram is just one method to analyze the validity of a syllogism. Other methods, such as Venn diagrams, truth tables, or logical rules, can also be used depending on the specific requirements or guidelines provided.