Answer
Inconsistent
Work Step by Step
Now, let's examine the statements:
1. Statement 1 (\( \neg R \)) states that \( R \) is false.
2. Statement 2 (\( (T \vee R) \wedge R \)) asserts that either \( T \) is true or \( R \) is true, and \( R \) must be true.
3. Statement 3 (\( (P \circ R \neg Q) \)) is not directly interpretable without knowing the meaning of the operator \( \circ \).
4. Statement 4 (\( (Q \vee R \neg T) \)) states that either \( Q \) is true or \( R \) is true but \( T \) is false.
5. Statement 5 (\( (R \vee R \neg P) \)) states that \( R \) is true or \( R \) is true but \( P \) is false.
Since \( R \) cannot simultaneously be true and false (contradiction), Statement 1 and Statement 2 cannot hold together. However, Statements 4 and 5 do not directly conflict with each other or with Statements 1 and 2.
The collection is inconsistent due to the contradiction between Statements 1 and 2. Therefore, the collection of statements is not consistent.
