- #1

McFluffy

- 37

- 1

"Consider the statement “If ##x > 2## then ## x^2 > 4##,” which we could represent with the formula ##P(x)→ Q(x)##,where ##P(x)## stands for the statement ##x > 2## and ##Q(x)## stands for ##x^2 > 4##. Of course, the statements ##P(x)## and ##Q(x)## contain ##x## as a free variable, and each will be true for some values of ##x## and false for others. But surely, no matter what the value of ##x## is, we would say it is true that ##\textit{if} ## ## x > 2## then ## x^2 > 4##, so the conditional statement ##P(x)→ Q(x)## should be true. Thus, the truth table should be completed in such a way that no matter what value we plug in for ##x##, this conditional statement comes out true."

I don't understand when he started to assert that no matter what values of ##x## the conditional comes out true. What does he mean by this? What am I missing?