The statement \( G \rightarrow \sim J \) is a contingency?

To determine whether the statement \( G \rightarrow \sim J \) is a contingency, we need to analyze its truth values under different interpretations of the propositions \( G \) and \( J \). 1. **Understanding the statement**: The statement \( G \rightarrow \sim J \) can be read as "If \( G \) is true, then \( J \) is false." This is a conditional statement. 2. **Truth table**: We can construct a truth table to evaluate the truth values of \( G \) and \( J \) and the resulting truth value of \( G \rightarrow \sim J \). | \( G \) | \( J \) | \( \sim J \) | \( G \rightarrow \sim J \) | |---------|---------|---------------|-----------------------------| | T | T | F | F | | T | F | T | T | | F | T | F | T | | F | F | T | T | 3. **Analyzing the truth table**: - When \( G \) is true and \( J \) is true, \( G \rightarrow \sim J \) is false. - When \( G \) is true and \( J \) is false, \( G \rightarrow \sim J \) is true. - When \( G \) is false (regardless of \( J \)), \( G \rightarrow \sim J \) is true. 4. **Conclusion**: The statement \( G \rightarrow \sim J \) is true in some cases and false in others. Therefore, it is not a tautology (which is always true) and not a contradiction (which is always false). Since it can be true for some truth assignments and false for others, it is classified as a **contingency**. Thus, the statement \( G \rightarrow \sim J \) is indeed a contingency.