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 need to analyze the truth table for the disjunction. In the truth table, "true" is represented by T and "false" by F.
1. The disjunction p v ~q is false when both p and ~q are false. So, p should be false, and ~q should be false as well.
2. The disjunction ~p v q is false when both ~p and q are false. To determine the values of p and q, we need to consider the negation of p. In this case, ~p is equivalent to "not p". So, if ~p is false, p should be true, and q should be false.
Therefore, the correct answers for your questions are:
1. When p v ~q is false, p is false, and q is false.
2. When ~p v q is false, p is true, and q is false.
Your answers were incorrect, but now you have the correct answers, and you understand how to determine them using the truth table for disjunctions.