Final Answer:
- a. P -> Q represents the original conditional statement.
- c. Q -> P represents the original conditional statement.
Step-by-step explanation:
The original conditional statement is "Doubling the dimensions of a rectangle increases the area by a factor of 4." This can be represented as P -> Q, where P is the statement "doubling the dimensions" and Q is the statement "increases the area by a factor of 4." Therefore, option a (P -> Q) correctly represents the original statement.
The inverse of the original conditional statement would be "Not doubling the dimensions does not result in an area increase by a factor of 4," which can be represented as P∼Q. However, this is not a valid representation of the inverse because the absence of doubling the dimensions doesn't necessarily imply the area won't increase by a factor of 4. So, option b (P∼Q) doesn't correctly represent the inverse.
Option c (Q -> P) represents the reverse form of the original statement, stating that "If the area increases by a factor of 4, then the dimensions are doubled." This is another way of expressing the original relationship, making it a correct representation of the original conditional statement.
Regarding options d and e, they respectively represent the converse (A∼D) and the contrapositive (P ~Q) of the original statement. The converse states, "If the dimensions are doubled, the area increases by a factor of 4," which may not always hold true. The contrapositive, "If the area does not increase by a factor of 4, then the dimensions are not doubled," does not always hold true either. Hence, neither represents the original statement accurately.