6.a) Consider the statement "The square of any odd integer is odd." L Rewrite the statemens in the form (Do not use the oethen.") (1 mark) I1. Write a negation forthe statement (2 marks) b) Let QUn) be the predicate: Q(n) : n divides 99 The domain is the set of positive integers. Write each of the following propositions in words, and determine whether it is truc or false. Justify your answer i. Q(11) i. Vn Q(n) (2 marks) (2 marks) Determine the truth value of the following statement. The domain of the variable consists real numbers. Show your work and justify your answers. c) (3 marks) d) Let Px) be the statement "x can speak Spanish" and let Q(x) be the statement "x knows the computer language Java. Express each of the following sentences symbolically in terms of P(x). 0(x), quantifiers, and logical operators. The domain consists of all students at your school. I Every student at your school either knows the computer language Java or can speak (2 marks) IL. There is a student at your school who cannot speak Spanish but who does know the (2 marks) Spanish. computer language Java 7 Consider the following argument. Let the domain consist of all students in a class. Fred is a student in this class. Fred has co-op experience can get a good job upon graduation. Therefore, someone in this class can get a good job upon graduation experience. Everyone who has co-op Let S(x)be "x is a student in this class." Let P(x) be "x has Co-op experience." Let G(x) be"x can get a good job upon graduation." Write the hypotheses and conclusion symbolically a) (4 marks) Show by using the rules of inference for quantified statements that the conclusion follows from the hypotheses. Indicate the rule of inference used for each step of the proof that you provide. b) (6 marks) page 3 of 3