Question 1177227
Let's break down each statement:

**Given:**

* p: "The sun is shining."
* q: "It is raining."

**a) ¬p ∨ q**

* **In words:** "The sun is not shining, or it is raining."
* **Truth value:**
    * To determine the truth value, we need to consider the individual parts:
        * ¬p: "The sun is not shining."
        * q: "It is raining."
    * The "∨" symbol represents "or," which is true if at least one of the statements is true.
    * Therefore, the statement is true if either the sun is not shining, or it is raining, or both. We can not give a definitive true or false without knowing the current state of the sun and rain.
    * Thus we say that the truth value is dependent on the actual truth values of p and q.

**b) ¬q ⇒ ¬p**

* **In words:** "If it is not raining, then the sun is not shining."
* **Truth value:**
    * To determine the truth value, we need to consider the individual parts:
        * ¬q: "It is not raining."
        * ¬p: "The sun is not shining."
    * The "⇒" symbol represents "implies" or "if...then."
    * An implication is only false when the antecedent (the "if" part) is true and the consequent (the "then" part) is false.
    * In this case, the statement is saying that the absence of rain implies the absence of sunshine. This is not necessarily true in the real world (the sun can be shining without rain, and the sun can be not shining without rain, and the sun can be not shining when it is raining).
    * Like the previous statement, the truth value is dependent on the actual truth values of p and q.

**Summary:**

* Both statements' truth values depend on the actual truth values of the propositions "The sun is shining" (p) and "It is raining" (q).
* In short, without knowing if it is raining or if the sun is shining, we can not assign a definitive true or false to either statement.