Question

Which of the following accurately describes the given statement "If a number is negative, the additive inverse is positive"?

A) If p represents a number being negative and q represents the additive inverse being positive, the original statement is p → q.

B) For all x, if p represents a number being negative and q represents the additive inverse being positive, the inverse of the original statement is "p → q."

C) If p represents a number being negative and q represents the additive inverse being positive, the converse of the original statement is →p.

D) If g represents a number being negative and p represents the additive inverse being positive, the contrapositive of the original statement is p~q.

E) If g represents a number being negative and p represents the additive inverse being positive, the converse of the original statement is →p.

Answer 1

The correct choice is A) If p represents a number being negative and q represents the additive inverse being positive, the original statement is p → q.

Step-by-step explanation:

The statement "If a number is negative, the additive inverse is positive" can be represented as a conditional statement. In symbolic logic, this statement is expressed as "p → q," where p represents a number being negative, and q represents the additive inverse being positive. Therefore, option A accurately describes the given statement.

In the symbolic representation "p → q," the arrow (→) indicates a conditional relationship. It asserts that if p (a number being negative) is true, then q (the additive inverse being positive) must also be true. This logical structure aligns with the original statement about negative numbers and their additive inverses.

Other choices (B, C, D, and E) introduce variations that do not precisely capture the conditional relationship described in the original statement. Therefore, option A is the most accurate representation of the given statement.

In conclusion, when translating verbal statements into symbolic logic, it is crucial to identify the correct conditional structure. Option A correctly represents the given statement by establishing a logical connection between a negative number and its positive additive inverse.

Therefore, the correct option is A.