In this exercise, let P and Q be predicates on a common domain of discourse. Mark all statements that must be true, no matter what P and Q are.

Group of answer choices

If P$($x$)$ is true for some x or Q$($x$)$ is true for some x$,$ then P$($x$)$Q$($x$)$ is true for some x$.$

If P$($x$)$Q$($x$)$ is true for some x$,$ then P$($x$)$ is true for some x$,$ or Q$($x$)$ is true for some x$.$

If P$($x$)$Q$($x$)$ is true for some x$,$ then P$($x$)$ is true for some x and Q$($x$)$ is true for some x$.$

If P$($x$)$ is true for some x and Q$($x$)$ is true for some x$,$ then P$($x$)$Q$($x$)$ is true for some x$.$