Decide whether the following predicate wffs is valid or inva

Decide whether the following predicate wffs is valid or invalid. If it is valid explain why; and if, it is invalid give an interpretation to justify your answer. (x)P(x) (x)Q(x) rightarrow (x)(P(x) Q(x))

Solution

The statement is TRUE

Since for every x in P(x), there exists a x in Q, implies that there must exists a x in P U Q, since for every x in P(x), the given statement is defined, hence for all x it must be inclined in PUQ as well, hence the statement will hold true for all cases