CSE 253 (Discrete Structure) Homework# 2 Due Date: Feb 24, 2021 Q#1: Let P(x) be the statement "x spends more than five hours every weekday in class." where the domain for x consists of all students. Express each of these quantifications in English a) 2xP(x) b) VxP(x) C) EXP(x) d) VxP(x) Q#2: Let p(x) and g(x, y) be the predicates P(x): x is your classfellow, g(x, y): x has taken the math course y If the domain of x is the set of all students in UoHB and the domain of y is the set of all math courses offered in UoHB. Write the following statements using symbolic notations: (a) Every student in your class has taken at least one math course. (b) No one at UoHB has taken all math courses. (c) There is a unique math course that has been taken by all students in your class. Q#3: What rule of inference is used in each of these arguments? a) Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials. b) It is either hotter than 100 degrees today or the pollution is dangerous. It is less than 100 degrees outside today. Therefore, the pollution is dangerous. C) 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. d) All men are mortal. Socrates is a man. Therefore, Socrates is mortal. e) No man is an island. Manhattan is an island. Therefore, Manhattan is not a man. Q#4: Let n is an integer. If n2+5 is odd, then n is even. Proof this theorem by using contradiction