Final answer:
Doubling the dimensions of a rectangle does increase the area by a factor of 4.
Step-by-step explanation:
The original conditional statement is p → q, which represents doubling the dimensions of a rectangle (p) and the area increasing by a factor of 4 (q). This statement is true since doubling the dimensions of a rectangle does in fact double both the length and width, resulting in a new area that is four times larger than the original area. Therefore, q → p also represents the original conditional statement, as it states that if the area increases by a factor of 4, then the dimensions of the rectangle have been doubled.
The inverse of the original conditional statement is ~p → ~q, which states that if the dimensions of a rectangle are not doubled, then the area does not increase by a factor of 4. This statement is false, as not doubling the dimensions of a rectangle does not guarantee that the area will not increase by a factor of 4. Similarly, the converse of the original conditional statement is ~q → ~p, which states that if the area does not increase by a factor of 4, then the dimensions of the rectangle are not doubled. This statement is also false, as the area not increasing by a factor of 4 does not imply that the dimensions have not been doubled.
The contrapositive of the original conditional statement is p → ~q, which states that if the dimensions of a rectangle are doubled, then the area does not increase by a factor of 4. This statement is also false, as doubling the dimensions of a rectangle does result in the area increasing by a factor of 4. Therefore, the correct options are p → q and q → p.
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