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?
To determine the values of p and q when a disjunction is false, we can analyze the statements given.
1. When p v ~q is false:
In a disjunction, for the entire statement to be false, both sides of the "or" must be false. So, if p v ~q is false, it means that both p and ~q must be false. Negation (~) of q means the opposite of the value of q. Therefore, when p v ~q is false, p is False (F) and q is True (T).
2. When ~p v q is false:
Similar to the previous case, for the entire statement to be false, both sides of the "or" must be false. So, if ~p v q is false, it means that both ~p and q must be false. Negation (~) of p means the opposite of the value of p. Therefore, when ~p v q is false, p is True (T), and q is False (F).
So, your answers should be:
1. When p v ~q is false, p is False (F), and q is True (T).
2. When ~p v q is false, p is True (T), and q is False (F).
You are correct!