Question

Use a truth table to determine whether the following is a tautology, a contradiction, or neither. ~PAP Q~QvQ

Answer 1

Answer:

The statement $\lnot P \land P \rightarrow Q \rightarrow\lnot Q\lor Q$ is a tautology.

Step-by-step explanation:

We have the following statement $\lnot P \land P \rightarrow Q \rightarrow\lnot Q\lor Q$

A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

The simple statements from the statement given are:

$\lnot P$, $\lnot Q$, $\lnot P \land P$, $\lnot P \land P \rightarrow Q$, and $\lnot Q \lor Q$ with these you can construct the following truth table.

A tautology is a formula that is always true, it is true for every assignment of truth values to its simple components.

The last column contains only true values. Therefore, the statement is a tautology.