Consider the function defined by the following arrow diagram: (1) What is the domain of  ? [a1] (2) What is the codomain of  ? [a2] (3) What is the range of  ? [a3] (4) Is  one-to-one? [a4] (5) Is  onto? [a5]

(6 points for the correct answer; 2 bonus point if you have correctly answered a total of 9 questions among questions 1 through 11.)  Consider the following proof of the fact that the sum of any two even integers is even:  Suppose  and  are any even integers. By definition of even,   and  for some integers  and . Then . Note that  is an integer because the sum of two integers is an integer. Hence  is an even integer by definition of even.  Is the proof valid? 

(6 points for the correct answer; 2 bonus point if you have correctly answered a total of 9 questions among questions 1 through 11.)  Consider the following proof of the fact that the product of any two odd integers is odd:  Suppose  and are any odd integers. By definition of odd,   and for some integers and . Then . Note that is an integer because the sums and products of integers are integers. Hence  is an odd integer by definition of odd.  Is the proof valid? 

(1) For any integers  and , if  and , then

(6 points for the correct answer; 2 bonus point if you have correctly answered a total of 9 questions among questions 1 through 10.)  Fill in the blanks in the following proof by contrapositive that    Proof by contrapositive: Suppose  is any integer such that [a1]. By definition,  [a2]. By substitution,  [a3]. But  is an integer because the sums and products of integers are integers. Hence,  is [a4] by definition of [a5]. 

Let sets and be defined as follows:

(1) For any integers  and , if  and , then . True or false? [a1] (2) There exist integers  and  such that if  and , then

Consider the Venn diagram: Which of the following sets represent(s) ? (1)

Define 

On October 1, 2020 Bartley Corporation purchased new equipment by signing a 2 year note payable with a face value of $8,000,000 and paying cash of $500,000.  The note does not state an interest rate.  The present value of the note payable is 7,750,000 on October 1, 2020.  The fair value of the new equipment is approximately $8.250 million.Bartley recorded this purchase on October 1, 2020.  Select ALL applicable answers below related to the initial recording of the new equipment.