- $\text{P}$
$\text{Answer:}$ not a tautology
- $\text{P} \Rightarrow \text{P}$
$\text{Answer:}$ tautology
- $(\text{P} \Rightarrow \text{P}) \Rightarrow \text{P}$
$\text{Answer:}$ not a tautology.
$\text{Example reasoning:}$
Not all rows in the truth table evaluate to true.
$$\begin{array}{|c|c|c|}\hline \text{P} & \text{P} \Rightarrow \text{P} & (\text{P}\Rightarrow \text{P})\Rightarrow \text{P} \\ \hline \text{T} & \text{T} & \text{T} \\\hline \text{F} & \text{T} & \text{F} \\\hline \end{array}$$
- $\text{P} \Rightarrow (\text{P} \Rightarrow \text{P})$
$\text{Answer:}$ tautology
Detailed Video Solution: https://youtu.be/nclBhBmtz2g?t=313