I have a question about disjunctions.

The symbol "v" represents "or". "~" stands for "negation of"
Here are two questions I need help with:
1. When p v ~q is false, then p is ______ and q is _____.
I think "false" belongs in both spaces.
2. When ~p v q is false, then p is ______ and q is ________.
I think "false" is the answer to both of these as well.
Am I correct?

In disjunctions, the statement is true if at least one of the connected propositions is true. Let's analyze your two questions:

1. When p v ~q is false, then p is ______ and q is _____.
To determine the truth value for this expression, we need to consider the possibilities of p and q.
If the statement "p v ~q" is false, it means that neither p nor ~q is true.
- If p is true, then ~q must be false (since p v ~q would be true).
- If p is false, then ~q must be true (since p v ~q would be true).
So, when "p v ~q" is false, p must be false, and q must be true.

Therefore, your answer is incorrect. When "p v ~q" is false, p is false, and q is true.

2. When ~p v q is false, then p is ______ and q is ________.
To determine the truth value for this expression, we need to consider the possibilities of p and q.
If the statement "~p v q" is false, it means that neither ~p nor q is true.
- If ~p is true, then q must be false (since ~p v q would be true).
- If ~p is false, then q must be true (since ~p v q would be true).
So, when "~p v q" is false, p must be true, and q must be false.

Therefore, your answer is incorrect. When "~p v q" is false, p is true, and q is false.

In both cases, the correct answers are different from your initial guesses.