Problem 3

For the following, assume $p$ and $q$ are statements. Which of the following are true statements?

1. $\forall p\;\forall q\;(p\equiv q)$.

2. $\forall p\;\exists q\;(p\equiv q)$.

3. $\exists p\;\forall q\;(p\equiv q)$.

4. $\exists p\;\exists q\;(p\equiv q)$.

5. $\forall p\;\forall q\;(p\not\equiv q)$.

6. $\forall p\;\exists q\;(p\not\equiv q)$.

7. $\exists p\;\forall q\;(p\not\equiv q)$.

8. $\exists p\;\exists q\;(p\not\equiv q)$.