Use rules of inference to show that if ∀x(p(x) ∨q(x)) and ∀x ((¬ p(x) ∧ q(x)) → r(x)) are true, then ∀x (¬ r(x) → p(x)) is also true, where the domains of all quantifiers are the same.

Tom is the deli manager at a grocery store. he needs to schedule employee to staff the deli department for no more that 260 person-hours per week. tom has one part-time employee who works 20 person-hours per week. each full-time employee works 40 person-hours per week. write and inequality to determine n, the number of full-time employees tom may schedule, so that his employees work on more than 260 person-hours per week. graph the solution set to this inequality.