Let's analyze the truth table to check if it is correct for the given logical statement $p \rightarrow \neg q$ (read as "if $p$, then not $q$").

Here’s how we approach the problem:

1. Given Statement: $p \rightarrow \neg q$

2. Negation of $q$ ($\neg q$):

   • $q = T$, then $\neg q = F$
   • $q = F$, then $\neg q = T$

3. Implication $p \rightarrow \neg q$:

   • Implication $p \rightarrow \neg q$ is false only if $p = T$ and $\neg q = F$ (i.e., $p = T$ and $q = T$). Otherwise, it is true.

Now, let's check the table:

Comparison with the provided table:

The table you uploaded shows:

It matches the correct truth table for $p \rightarrow \neg q$, so yes, the truth table is correct.

Would you like more details on truth tables or implications? Here are some related questions:

1. How does the implication $p \rightarrow q$ work logically?
2. What happens if both $p$ and $q$ are false in an implication?
3. Can you explain the difference between $p \rightarrow q$ and $q \rightarrow p$?
4. What is the significance of the negation $\neg q$ in logical statements?
5. How would a truth table look for the expression $\neg (p \wedge q)$?

Tip: In logic, an implication is only false when the first part is true, and the second part is false.