Answer all

1. Consider the following statement which is true. If n is any odd integer, then 2n is even. (a) Write the converse of the statement. (2 marks) (b) Give a counterexample to show that the converse is false. (2 marks) 2. Let P(n) and Q) be predicates given below and the domain of n is Z. Let P(n) represent: 6 is an integer Let Q(n) represent: n=3 Vinteger n, if 6 is an integer then n = 3 (a) Write the statement symbolically, and using P(n) and Q(a). (2 marks) (6) Write the negation for the statement obtained in (a), showing each step carefully (3 marks) (c) Write the answer obtained in (b) informally (1 mark) 3. Determine whether the following argument is valid or invalid. Justify your answer. (2 marks) For every student x, if x is a first-year student, then x must take an English course, Rita is a first-year student. Therefore, Rita must take an English course