use the euler diagram to determine if the syllogism is valid or invalid
1. Football and studying don't mix
Don is football player.
therefore: Don does not study
To use an Euler diagram to determine the validity of the syllogism, we need to represent the information given in the statements visually.
Step 1: Create the Diagram
Draw two overlapping circlesโone representing "Football" and the other representing "Studying." Make sure there is an area where the two circles overlap, as it will be necessary for determining the validity.
Step 2: Represent the Statements
Label the circle corresponding to "Football" and write "Don" inside it. This represents the fact that Don is a football player.
Step 3: Analyze the Inference
According to the syllogism, "Football and studying don't mix." This means that if someone is involved with football, they cannot study simultaneously. Therefore, we need to check if the statement "Don does not study" aligns with the information represented in the diagram.
Step 4: Determine Validity
If we see that Don is inside the "Football" circle and outside the overlapping region, it indicates that he does not study, and the syllogism is valid.
In this case, the Euler diagram confirms the validity of the syllogism, as Don is depicted as participating in football but not in the area of the diagram representing studying.