Given the argument and its Euler diagram, determine the syllogism is valid or invalid.
Those who play football.
don
Football and studying don�ft mix
Those who studt
Don is a football player
�ˆdon does not study
want to try that again in English?
To determine whether the syllogism is valid or invalid, we need to analyze the argument and refer to the given Euler diagram. Let's break down the argument and map it out using the diagram:
Premise 1: "Those who play football."
This statement indicates a group of people who play football. We can represent it in the Euler diagram by shading a portion that represents football players.
Premise 2: "Football and studying don't mix."
This statement suggests that studying is not compatible with playing football. We don't need to represent this in the diagram since it describes the relationship between football and studying.
Premise 3: "Those who study."
This statement refers to a group of people who study. We can represent it in the diagram by shading another portion that represents students.
Premise 4: "Don is a football player."
This statement asserts that Don is a member of the group of people who play football. We can mark the portion representing football players in the diagram to indicate Don's association with that group.
Premise 5: "Don does not study."
This statement claims that Don does not belong to the group of people who study. However, we don't need to modify the diagram to represent this information since it doesn't directly relate to the diagram's elements.
Now, let's analyze the conclusion implied by these premises:
Conclusion: Don does not studt.
Based on the given premises, we can infer that Don does not study because he is not a member of the group that studies.
To determine the validity of the syllogism, we need to check if the conclusion logically follows from the given premises and diagram. In this case, the conclusion "Don does not study" does indeed logically follow from the information provided. Therefore, the syllogism is valid based on the given arguments and Euler diagram.