Discrete Mathmatics

4. What rule of inference is used in each of these arguments? a) Kangaroos live in Australia and are marsupials. There- fore, kangaroos are marsupials. It is either hotter than 100 degrees today or the pollu- tion is dangerous. It is less than 100 degrees outside today. Therefore, the pollution is dangerous Linda is an excellent swimmer. If Linda is an excellent swimmer, then she can work as a lifeguard. Therefore, Linda can work as a lifeguard b) c) d) Steve will work at a computer company this summer. Therefore, this summer Steve will work at a computer company or he will be a beach bumm e) If I work all night on this homework, then I can an swer all the exercises. If I answer all the exercises, I will understand the material. Therefore, if I work all night on this homework, then I will understand the material 28. Use rules of inference to show that if Vx(P(x) V Q(x)) and yx((+P(x) Q(x))-> R(x)) are true, then Vx(-R(x) -P(x) is also true, where the domains of all quantifiers are the same