Answer:
The three options are;
1) When p represents a negative number and q represents its positive additive inverse, the original expression is p → q.
2) When p is a negative number and q is the positive additive inverse, the inverse of that statement is ~p → ~q.
3) When q represents a negative number and p its positive additive inverse, the contrapositive of the original statement is ~p → ~q.
Step-by-step explanation:
Based on the statement if p implies q, we can denote it as p → q. The converse becomes q → p, while the inverse is ~p → ~q, and the contrapositive is ~q → ~p.
Mathematically expressed;
The initial conditional statement;
If a number is negative, then the additive inverse is positive, which is presented as;
The conditional statement is p → q.
The converse statement is q → p.
The inverse statement is ~p → ~q.
The contrapositive statement is ~q → ~p.
Thus, we conclude;
1) The conditional statement indicates that when p is negative and q is the positive additive inverse, it's p → q.
2) When p is a negative number and q is the positive additive inverse, the conditional expression p → q leads to the inverse being ~p → ~q.
3) If q is negative and p is the positive additive inverse, the original statement shows it as q → p, making the contrapositive representation ~p → ~q.
