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) Q(x)) rightarrow (x)P(x) (x)Q(x)

Solution

The given statement is TRUE

Since there exists a x for PUQ, implies either the statement P(x) is true or Q(x) is true in order to make PUQ to be true

Hence the statement can be bisected into two parts, therefore the given statement holds true