Questions: Use Euler diagrams to determine whether the following argument is valid or invalid. All English professors are good readers. J.R.R. Tolkien is one of the English professors. Therefore, J.R.R. Tolkien is one of the good readers. Choose the correct answer below. Invalid Valid

Use Euler diagrams to determine whether the following argument is valid or invalid.
All English professors are good readers.
J.R.R. Tolkien is one of the English professors.

Therefore, J.R.R. Tolkien is one of the good readers.

Choose the correct answer below.
Invalid
Valid

Transcript text: Use Euler diagrams to determine whether the following argument is valid or invalid. All English professors are good readers. J.R.R. Tolkien is one of the English professors. Therefore, J.R.R. Tolkien is one of the good readers. Choose the correct answer below. Invalid Valid

Solution

Solution Steps

To determine the validity of the argument using Euler diagrams, we need to visualize the relationships between the sets involved. We have three sets: English professors, good readers, and J.R.R. Tolkien. The statement "All English professors are good readers" suggests that the set of English professors is entirely within the set of good readers. The statement "J.R.R. Tolkien is one of the English professors" places J.R.R. Tolkien within the set of English professors. Therefore, J.R.R. Tolkien must also be within the set of good readers, making the argument valid.

Step 1: Define the Sets

Let \( E \) represent the set of English professors and \( G \) represent the set of good readers. We know from the argument that: \[ E \subseteq G \] This means that all elements of set \( E \) are also elements of set \( G \).

Step 2: Identify the Element

We are given that: \[ J.R.R. Tolkien \in E \] This indicates that J.R.R. Tolkien is an English professor.

Step 3: Conclusion

Since \( J.R.R. Tolkien \) is an element of \( E \) and \( E \subseteq G \), it follows that: \[ J.R.R. Tolkien \in G \] Thus, J.R.R. Tolkien is also a good reader.