This is a geometry 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?
Is this how geometry is taught these days? It looks like symbolic logic to me.
I believe the answers are:
1. false; true
2. true; false
However I am interpreting the v ("or") symbol as also meaning "and".
I don't see how you can logically convert an "or" statemen to an "and" statement as you have done
I am not converting them to "and" statements. I am breaking apart statements p and q individually. These are 'disjunctions', did you know that? I'm just trying to see if we're on the same page.
To answer these questions, we need to analyze the given logical statements and understand the conditions under which they are false. Let's break down each statement and determine the values of p and q that make them false.
1. Statement: p v ~q
- This statement is false when neither p nor ~q is true.
- When p is false and ~q is false, the statement becomes false.
- Therefore, p is false (not true) and q is true.
2. Statement: ~p v q
- This statement is false when neither ~p nor q is true.
- When ~p is false and q is false, the statement becomes false.
- Therefore, p is true and q is false (not true).
Based on the analysis above, the correct answers are:
1. When p v ~q is false, p is false and q is true.
2. When ~p v q is false, p is true and q is false.
Therefore, your answer for question 1 is incorrect. For question 2, you have correctly identified that p is true, but the answer for q is false instead of false.