The problem asks to evaluate the truth value of the logical expression:

$(p \rightarrow q) \oplus (q \rightarrow p)$

Given that:

• $p$ is false,
• $q$ is true.

We need to break down each part of the expression:

1. Implication $p \rightarrow q$:

   • The implication $p \rightarrow q$ is true when $p$ is false, regardless of $q$'s truth value. Since $p$ is false and $q$ is true, $p \rightarrow q$ is true.

2. Implication $q \rightarrow p$:

   • The implication $q \rightarrow p$ is false when $q$ is true and $p$ is false. Since $q$ is true and $p$ is false, $q \rightarrow p$ is false.

3. Exclusive OR (XOR, $\oplus$):

   • The XOR operation is true if one of the operands is true and the other is false. Since $p \rightarrow q$ is true and $q \rightarrow p$ is false, the XOR evaluates to true.

Thus, the truth value of the expression is true.

Let me know if you'd like further clarification or details! Here are five related questions to explore:

1. What are the truth tables for the logical operations $\rightarrow$ and $\oplus$?
2. How does the truth value of $p \rightarrow q$ change if both $p$ and $q$ are true?
3. What happens if both $p$ and $q$ are false in the expression $(p \rightarrow q) \oplus (q \rightarrow p)$?
4. Can you give another example where XOR between two implications results in false?
5. What is the difference between the logical operations AND, OR, and XOR?

Tip: In logic, implications ($\rightarrow$) are always true when the premise is false, no matter the conclusion.