Find logical equivalent

Question

I know the statement given in question means "p is true if p or are true""

But now how to proceed .

Can we solve it using truth table

Answer 1

The easiest way to realize this is that the statement $p\rightarrow (p\lor q)$ is a tautology (i true no matter what $p$ or $q$ is). This can be seen as if $p$ is true then of course $p\lor q$ is true too.

The answer must for that reason be a tautology. That no other than (3) is is easy to see, fx if both $p$ and $q$ is true then (4) is false. You see that (3) is a tautology since if $q$ is true, then no matter what $p$ is $p\rightarrow q$ must be true.

Perhaps it's easier to see if you create a truth table (the $p\lor q$ and $p\rightarrow q$ columns are only intermediate in constructing the next column):

$$\begin{matrix} p & q & p\lor q & p\rightarrow (p\lor q) & p\rightarrow q & q\rightarrow(p\rightarrow q) \\ \hline f & f & f & T & T & T \\ f & T & T & T & T & T \\ T & f & T & T & f & T \\ T & T & T & T & T & T \\ \end{matrix}$$