9. Create a Euler diagram to determine whether the syllogism is valid or invalid.
All children like games.
John likes games.
John is a child., <--At the beginning of this sentence which is the last sentence is suppose to have three dots shaped like a triangle. (I am having problems creating a Euler diagram. If anyone can please help.)
invalid conclusion
all we know is that children like games. tells us nothing about John.
To determine whether the syllogism is valid or invalid using a Euler diagram, we can start by creating a diagram to represent the given statements. Here's a step-by-step guide:
Step 1: Draw a rectangle to represent the universal set, which in this case could be "people" or "individuals."
Step 2: Inside the rectangle, draw a smaller circle to represent the set of children. Label it "Children."
Step 3: Now, draw another circle partially overlapping with the "Children" circle to represent the set of people who like games. Label it "People who like games."
Step 4: Inside the "Children" circle, indicate John as a specific element.
The final diagram should have two circles, one labeled "Children" and the other labeled "People who like games." There is an overlap between the two circles, indicating that there are children who like games. Inside the "Children" circle, John should be indicated as a specific element.
Please note that Euler diagrams are just one visualization tool, and the validity of a syllogism cannot be determined solely based on the diagram. It's important to use logical reasoning as well.
Hope this helps!
To determine the validity of the syllogism using a Euler diagram, you would generally follow these steps:
Step 1: Identify the categorical statements in the syllogism. Categorical statements are statements about the relationship between two or more classes (groups) of objects or things. In the given syllogism, we have the following categorical statements:
- All children like games. (This can be represented as: All children are in the "children who like games" circle)
- John likes games. (This can be represented as: John is in the "people who like games" circle)
- John is a child. (This can be represented as: John is in the "children" circle)
Step 2: Determine the overlapping areas by creating circles or ellipses that represent the classes mentioned in the syllogism. Make sure to label them accordingly (e.g., "children who like games", "children", "people who like games").
Step 3: Place the elements (in this case, John) into the appropriate areas of the diagram based on the given statements. In this case, you would place John within the "children who like games" circle and the "children" circle since he is both a child and likes games.
Step 4: Evaluate if the diagram supports the statements in the syllogism. If all the elements in the diagram align with the statements, then the syllogism is considered valid. If there is a contradiction (i.e., an element does not fit the statements), then the syllogism is considered invalid.
Remember, Euler diagrams are used to visually represent the relationships between classes or groups based on categorical statements. They can be helpful tools for understanding a syllogism, but they are not the only method for evaluating its validity.