Question

Let A be a formula in which the variables p, q,r occur, but no others, and whose truth table has a result t only in the rows f, t, f (state for p, q, r in that order) and t, f, f. Show that A is provably equivalent to the formula: p Aq¬rvp¬qr.

Answer 1

To show that A is provably equivalent to the formula p Aq¬rvp¬qr, we need to prove that both formulas have the same truth table. By creating a truth table for both formulas, we can see that they indeed have the same truth values in every row.

Step-by-step explanation:

In order to show that A is provably equivalent to the formula p Aq¬rvp¬qr, we need to prove that both formulas have the same truth table. We can start by creating a truth table for A and p Aq¬rvp¬qr:

pqrAp Aq¬rvp¬qrfffttftffffftttftttttffttttffftftttttttt

As you can see, both formulas have the same truth table. Therefore, we can conclude that A is provably equivalent to the formula p Aq¬rvp¬qr.