Question

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

Answer 1

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

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.