Final answer:
Option (a) correctly represents the original conditional statement where doubling the dimensions of a rectangle leads to the area increasing by a factor of four. Option (b) provides the inverse of the original conditional statement, which negates both the hypothesis and the conclusion.
Step-by-step explanation:
When we discuss the effects of doubling the dimensions of a rectangle, we see a corresponding increase in its area by a factor of four. If p represents the action of doubling the dimensions, and q represents the area of the rectangle increasing by a factor of four, we can analyze the logical statements provided.
Option (a), which states p → q, represents the original conditional statement. This is a direct translation: if the dimensions are doubled (p), then the area increases by a factor of four (q).
Option (d), ~q → ~p, represents the converse of the original conditional statement. In logical terms, the converse flips the original conditional but does not negate the terms. Therefore, this option is incorrect as it also negates the original terms.
The correct answers are, therefore, option (a) p → q, the original conditional statement, and option (b) ~p → ~q, which represents the inverse of the original conditional statement. The inverse negates both the hypothesis and the conclusion of the conditional statement.