(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.

The balanced scorecard evaluation of the firm is an especially strong financial tool because of its:

A system of government in which ultimate political power lies within the state

The process of using social science methods to get an accurate sense of the public’s view about an issue.