Discrete Mathmatics

28. Use rules of inference to show that if Vx(P(x) v Q(x)) and yx((7P(x) Q(x))-> R(x)) are true, then Vy (R(x) P (x)) is also true, where the domains of all quantifiers are the same. 10. Use a direct proof to show that the product of two rational numbers is rational 22. Show that if you pick three socks from a drawer contain- ing just blue socks and black socks, you must get either a pair of blue socks or a pair of black socks