Let's create two statements and determine the truth value for $\neg p \lor \neg q$ (the logical OR of the negations of $p$ and $q$).

Statements:

• $p$: "The sky is blue."
• $q$: "The sun is shining."

Assigning Truth Values:

• $p$ ("The sky is blue"): This statement is true (assuming it's a clear day).
• $q$ ("The sun is shining"): This statement is also true (assuming it's daytime and clear).

Negations:

• $\neg p$: "The sky is not blue." This is false because the sky is blue.
• $\neg q$: "The sun is not shining." This is false because the sun is shining.

Finding $\neg p \lor \neg q$:

The statement $\neg p \lor \neg q$ is true if at least one of $\neg p$ or $\neg q$ is true.

• Since both $\neg p$ and $\neg q$ are false, $\neg p \lor \neg q$ is false.

Summary:

• $\neg p \lor \neg q$ is false.

Would you like more details or have any further questions?

Relative Questions:

1. What is the truth value of $\neg p \land \neg q$ for the given statements?
2. How would the truth value of $\neg p \lor \neg q$ change if $q$ were false?
3. What is the truth value of $\neg(\neg p \lor \neg q)$ for the given statements?
4. How would the truth value of $p \lor \neg q$ be affected if $p$ were false?
5. Can $\neg p \land q$ ever be true? Under what conditions?

Tip:

When dealing with logical negations, it’s helpful to first determine the truth value of the original statements before applying the negation. This makes it easier to evaluate more complex logical expressions like $\neg p \lor \neg q$.