Question

use the truth table to determine if ~(p ∧ q)≡~p ∨ ~q
yes, these statements are equivalent
there is not enough information to determine if the statements are equivalent.
no, these statements are not equivalent.

Explanation:

Step1: Analyze truth - table columns

Check the columns for $
eg(p\wedge q)$ and $
eg p\vee
eg q$.

Step2: Compare truth - values

For all combinations of truth - values of $p$ and $q$, the truth - values of $
eg(p\wedge q)$ and $
eg p\vee
eg q$ are the same. When $p = T,q = T$, $
eg(p\wedge q)=F$ and $
eg p\vee
eg q = F$. When $p = T,q = F$, $
eg(p\wedge q)=T$ and $
eg p\vee
eg q = T$. When $p = F,q = T$, $
eg(p\wedge q)=T$ and $
eg p\vee
eg q = T$. When $p = F,q = F$, $
eg(p\wedge q)=T$ and $
eg p\vee
eg q = T$.

Answer:

Yes, these statements are equivalent