Question

Suppose that during the most recent fiscal year, the annual revenue of Acme Computer was billion dollars and its net profit was billion dollars, the annual revenue of Nadir Software was billion dollars and its net profit was billion dollars, and the annual revenue of Quixote Media was billion dollars and its net profit was billion dollars. Determine the truth value of each of these propositions for the most recent fiscal year.

1. Quixote Media had the largest annual revenue.
2. Nadir Software had the lowest net profit and Acme Computer had the largest annual revenue.
3. Acme Computer had the largest net profit or Quixote Media had the largest net profit.
4. If Quixote Media had the smallest net profit, then Acme Computer had the largest annual revenue.
5. Nadir Software had the smallest net profit if and only if Acme Computer had the largest annual revenue.

Short answer

1. The statement is false
2. The statement is true
3. The statement is true
4. The statement is true.
5. The statement is true

Step-by-step solution

Definition of proposition

Proposition:
1. It is a declarative statement which can be either true or false.
2. It cannot be both true and false simultaneously

Truth value of statement in a)

Quixote Media did not have the largest annual revenue.

The truth value of the statement is false.

Truth value of statement in b)

Nadir Software had the lowest net profit is true and Acme Computer had the largest annual revenue is also true.

Hence, True and True is True.

The truth value of statement is true.

Truth value of statement in c)

Acme Computer had the largest net profit is false or Quixote Media had the largest net profitis true. Since False or True is true.

The truth value of the statement is true.

Truth value of statement in d)

If Quixote Media had the smallest net profit, then Acme Computer had the largest annual revenue. Here it is$F\to T$ is True.

The truth value of the statement is true.

Truth value of statement in e)

Nadir Software had the smallest net profit if and only if Acme Computer had the largest annual revenue. Here it is$T\leftrightarrow T$is true.

The truth value of the statement is true.