To construct a truth table for the statement $( (p \lor q) \land \neg r ) \rightarrow p$, we’ll go through each possible combination of truth values for $p$, $q$, and $r$ and determine the value of the entire expression.

Steps to complete the truth table:

1. Determine all possible combinations of truth values for $p$, $q$, and $r$.
2. Calculate $p \lor q$ for each combination.
3. Calculate $\neg r$ for each combination.
4. Calculate $(p \lor q) \land \neg r$.
5. Evaluate $( (p \lor q) \land \neg r ) \rightarrow p$.

The truth table structure will look like this:

$p$	$q$	$r$	$p \lor q$	$\neg r$	$(p \lor q) \land \neg r$	$((p \lor q) \land \neg r) \rightarrow p$
T	T	T	T	F	F	T
T	T	F	T	T	T	T
T	F	T	T	F	F	T
T	F	F	T	T	T	T
F	T	T	T	F	F	T
F	T	F	T	T	T	F
F	F	T	F	F	F	T
F	F	F	F	T	F	T

Determining if the Statement is a Tautology

For a statement to be a tautology, the final column should contain only true (T) values. Here, the final column has a single false (F) outcome in row 6, meaning the statement is not a tautology.

Would you like me to explain any specific steps in this table?

Here are five questions for further exploration:

1. How does negation impact the truth values of a statement?
2. What makes a logical statement a tautology?
3. How would the truth table change if we replaced $\lor$ (or) with $\land$ (and)?
4. What is the significance of the conditional statement ($\rightarrow$) in logic?
5. Can we create a truth table for other logical statements like biconditionals ($\leftrightarrow$)?

Tip: Practice constructing truth tables to get familiar with identifying tautologies and contradictions efficiently.