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 P(x) U Q(x) will be true only when either of P(x) is true or Q(x) is true

Hence when the PUQ is true implies either of them must be 1, therefore the given statement is TRUE