Final answer:
The contrapositive of the statement "If I use my cellphone too much, my bill will be expensive" is "If my bill is not expensive, I did not use my cellphone too much."Option D is the correct answer.
Step-by-step explanation:
In logic, the conditional statement "If I use my cellphone too much, my bill will be expensive" can be represented as: If P, then Q.
To find the statement that must be true if this conditional is true, we need to look for the statement that is the contrapositive of the conditional statement. The contrapositive of the conditional statement is: If not Q, then not P.
Therefore, the statement that must also be true if the conditional statement is true is: D. If my bill is not expensive, I did not use my cellphone too much.
In the realm of logic, the conditional statement "If I use my cellphone too much, my bill will be expensive" is symbolized as "If P, then Q." In this scenario, P represents the action of using the cellphone excessively, and Q denotes the consequence of incurring an expensive bill.
To identify the statement that must be true if the initial conditional statement holds, we turn to the contrapositive, which is framed as "If not Q, then not P." In practical terms, this translates to: "If my bill is not expensive, I did not use my cellphone too much" (option D). This contrapositive statement aligns with the logic of the original conditional and represents a valid inference derived from the given logical relationship.