Convert the compound statement into words.
p = Students are happy.
q = Teachers are happy.
~(p V ~q)
~q = Teachers are not happy.
p V ~q = Students are happy, or teachers are not happy.
~(p V ~q) = Students are not happy, or teachers are happy.
Wait!!! I take that back.
~(pV~q)=~p&q
so students and teachers are not happy?
To convert the compound statement ~ (p V ~q) into words, we can break it down step by step:
1. Start with the expression inside the parentheses: p V ~q.
- The "V" symbol represents the logical OR, which means either p or ~q (not q) is true, or both can be true.
- To understand p V ~q, we take the statements p and ~q separately.
2. Breaking down p and ~q:
- Given p = Students are happy, it means that the students are happy.
- Given q = Teachers are happy, ~q means that teachers are not happy.
3. Combining the two expressions:
- p V ~q translates to "Students are happy or teachers are not happy."
4. Finally, add the negation symbol "~" before the entire expression:
- ~(p V ~q) translates to "It is not the case that students are happy or teachers are not happy."
- Alternatively, it can be rephrased as "Neither students are happy nor teachers are not happy."