Question

Given the original statement "If a number is negative, the additive inverse is positive," which are true? Select three options. If p = a number is negative and q = the additive inverse is positive, the original statement is p - q. If p= a number is negative and q = the additive inverse is positive, the inverse of the original statement is up - -9. If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is - mp. If q= a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is p - 29. If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is a - p. Save and Exit Next Subm

Answer 1

1. The original statement p - q is true.

2. The inverse of the original statement is not up - -9.

3. The contrapositive of the original statement is p - 29.

Step-by-step explanation:

The original statement is "If a number is negative, the additive inverse is positive," which can be represented as p - q, where p is the event of a number being negative, and q is the event of the additive inverse being positive. Thus, p - q is a correct representation of the original statement.

Now, the inverse of the original statement is the negation of both p and q, represented as ¬p - ¬q. In this case, ¬p is "a number is not negative," and ¬q is "the additive inverse is not positive." It does not translate to up - -9, making option 2 incorrect.

The contrapositive of the original statement is ¬q - ¬p, meaning "the additive inverse is not positive implies that the number is not negative." This is correctly represented as p - 29, making option 3 true.

In summary, the correct interpretations are:

1. The original statement p - q is true.

2. The inverse of the original statement is not up - -9.

3. The contrapositive of the original statement is p - 29.