Prove or disprove the following predicate wffs is valid usin

Prove or disprove the following predicate wffs is valid using derivation rules. If the predicate wff is invalid, give an interpretation that satisfy your claim. (x)(P(x) rightarrow Q(x)) rightarrow [(x) P(x) rightarrow (x)Q(x)]

Solution

The LHS statement implies there exists a x for which P(x) implies Q(x)

The RHS statement implies that for every x belonging to P(x) there exists a x in Q(x)

The statement is TRUE, since if for x where P(x) implies Q(x) then there will be all x which will be connected with some Q(x)

Hence the statement is TRUE