Certainly! Let's look at each statement and complete the table step-by-step.
1. Statement [tex]\( p \)[/tex]: Pigs can fly.
- Based on everyday knowledge, pigs cannot fly.
- Therefore, [tex]\( p \)[/tex] is False.
2. Statement [tex]\( q \)[/tex]: Dolphins can swim.
- It is a well-known fact that dolphins can swim.
- Therefore, [tex]\( q \)[/tex] is True.
Next, let's analyze the logical connectives involving [tex]\( p \)[/tex] and [tex]\( q \)[/tex]:
3. Statement [tex]\( p \wedge q \)[/tex] (Logical AND):
- The logical AND operation ([tex]\(\wedge\)[/tex]) is true if and only if both [tex]\( p \)[/tex] and [tex]\( q \)[/tex] are true.
- Here, [tex]\( p \)[/tex] is False and [tex]\( q \)[/tex] is True.
- Since [tex]\( p \)[/tex] is False, [tex]\( p \wedge q \)[/tex] must be False (because for AND to be true, both operands must be true).
4. Statement [tex]\( p \vee q \)[/tex] (Logical OR):
- The logical OR operation ([tex]\(\vee\)[/tex]) is true if at least one of [tex]\( p \)[/tex] or [tex]\( q \)[/tex] is true.
- Here, [tex]\( p \)[/tex] is False and [tex]\( q \)[/tex] is True.
- Since [tex]\( q \)[/tex] is True, [tex]\( p \vee q \)[/tex] must be True (because for OR to be true, at least one of the operands must be true).
Now, we can fill the table with these values:
[tex]\[
\begin{tabular}{|l|l|}
\hline
$p$ & \text{False} \\
\hline
$q$ & \text{True} \\
\hline
$p \wedge q$ & \text{False} \\
\hline
$p \vee q$ & \text{True} \\
\hline
\end{tabular}
\][/tex]
So, the completed table is:
- [tex]\( p \)[/tex]: False
- [tex]\( q \)[/tex]: True
- [tex]\( p \wedge q \)[/tex] (Logical AND): False
- [tex]\( p \vee q \)[/tex] (Logical OR): True
