Question

Suppose that during the most recent fiscal year, the an- nual revenue of Acme Computer was 138 billion dollars and its net profit was 8 billion dollars, the annual revenue of Nadir Software was 87 billion dollars and its net profit was 5 billion dollars, and the annual revenue of Quixote Media was 111 billion dollars and its net profit was 13 billion dollars. Determine the truth value of each of these propositions for the most recent fiscal year.

a) Quixote Media had the largest annual revenue.
b) Nadir Software had the lowest net profit and Acme Computer had the largest annual revenue.
c) AcmeComputerhadthelargestnetprofitorQuixote Media had the largest net profit.
d) If Quixote Media had the smallest net profit, then Acme Computer had the largest annual revenue.
e) Nadir Software had the smallest net profit if and only if Acme Computer had the largest annual revenue.

Answer 1

Upon comparing the annual revenue and net profit of the companies, it was determined that Quixote Media did not have the largest annual revenue, Nadir Software did have the lowest net profit while Acme Computer had the largest annual revenue, and Acme Computer did not have the largest net profit but Quixote Media did.

Step-by-step explanation:

To determine the truth value of each proposition for the most recent fiscal year, we must compare the annual revenue and net profit of each company mentioned.

a) Quixote Media had an annual revenue of 111 billion dollars which is not the largest when compared to Acme Computer's 138 billion dollars. Therefore, the proposition is false.

b) Nadir Software had the lowest net profit at 5 billion dollars and Acme Computer had the largest annual revenue with 138 billion dollars. Thus, this proposition is true.

c) Acme Computer had the largest net profit at 8 billion dollars and Quixote Media had a net profit of 13 billion dollars. Since Quixote Media's net profit is larger, the proposition is true.

d) Since Quixote Media did not have the smallest net profit (it was the largest), the condition is not met, making this proposition irrelevant (the antecedent is false).

e) Nadir Software did not have the smallest net profit; it was Acme Computer. However, Acme Computer did have the largest annual revenue. Since the statement is a biconditional and one of the conditions is not met, the overall proposition is false.

Answer 2

a) False

b) True

c) True

d) False

e) True

Step-by-step explanation:

A– Acme computer has the largest annual revenue.

B– (x˄y) = If X = Y = 1 then 1; otherwise = 0. Both parts of equation are True, then the proposition is True.

C– (x˅y) = If X = Y = 0 then 0; otherwise = 1. The first part of the equation is False, and the second part is True, then the proposition is True.

D– (x→y) = If X = 1 and Y = 0, then (x→y) = 1. The first part of the equation is False, and the second part is True, then the proposition is False.

E- (x≡y) = If X = 0 and Y = 0, then (x≡y) = 0. Both parts of equation are True, then the proposition is True.