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

Answer:

a) False

b) True  

c) True

d) False

e) True

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.