Question

Complete the following sentence with true or false to make a correct statement.

When r → (∼p ∨ q) is false, p must be false, q must be true, and r must be true.

Answer 1

The statement 'When r → (∼p ∨ q) is false, p must be false, q must be true, and r must be true' is false. The truth values of p and q cannot be determined based solely on the falsity of r → (∼p ∨ q).

Step-by-step explanation:

The statement 'When r → (∼p ∨ q) is false, p must be false, q must be true, and r must be true' is false.

To make a correct statement, we can rewrite it as follows:

If r is true, then either p must be true or q must be false.

In this case, if r → (∼p ∨ q) is false, it means that the condition 'r is true' is true, but the outcome 'p must be true or q must be false' is not satisfied.

Therefore, we cannot determine the truth values of p and q based solely on the falsity of r → (∼p ∨ q). It is possible for p and q to have any combination of truth values.