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
A
If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.
B
If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
C
If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p.
D
If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
E
If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.
Explanation
Let p mean “the number is negative” and q mean “its additive inverse is positive.” The original statement is p → q, so A is true; its inverse is ~p → ~q, making B true. In D, the variables are assigned the other way around: q is “the number is negative” and p is “the additive inverse is positive,” so the original is q → p and its contrapositive is ~p → ~q. C gives the contrapositive rather than the converse, and E gives the original statement rather than its converse.
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