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 ~p → ~q.
If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p.
If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.

Answer 1

Correct choices: 1, 2, and 4.

Brief justification:
- 1: With p = “a number is negative” and q = “the additive inverse is positive,” the original statement is p → q. (True.)
- 2: The inverse of p → q is ~p → ~q. (True.)
- 4: If you relabel so q = “a number is negative” and p = “the additive inverse is positive,” then the original becomes q → p, whose contrapositive is ~p → ~q. (True.)

Options 3 and 5 are incorrect (3 mistakes converse for ~q → ~p; 5 mislabels the converse).