Hi,

I have the following task:

"Show thatPa V Pb -> Ex Px" where E stands for the existential quantifier.

I have done the following:

- Let M denote a model with domain D, and assume that M |= Pa V Pb

- It suffices then to show that M |= Ex Px

- Let s be an element in D, arbitrarily chosen

- By assumption, we know that M |= Ps(since we consider disjunction, it suffices to only include one, from Pa V Pb)

- Thus, it is the case that M |= Ex Ps- Since s was arbitrarily chosen, it will be so that M |= Ex Px, that Ex Px is true in M.

Is this the right way to prove validity?