Question

Read the statement.

Doubling the dimensions of a rectangle increases the area by a factor of 4.

If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are true? Select two options.

A. p → q represents the original conditional statement.
B. ~p → ~q represents the inverse of the original conditional statement.
C. q → p represents the original conditional statement.
D. ~q → ~p represents the converse of the original conditional statement.
E. p → ~q represents the contrapositive of the original conditional statement

Answer 1

Options A (p → q) and D (~q → ~p) are correct as A represents the original conditional statement, where doubling the dimensions of a rectangle leads to a quadrupling of its area, and D represents the converse of the original conditional statement.

Step-by-step explanation:

The original statement is that doubling the dimensions of a rectangle increases the area by a factor of 4. In logical terms, this is expressed as p → q, where p represents the act of doubling the dimensions and q represents the area increasing by a factor of 4.

Option A, p → q, is correct as it represents the original conditional statement. If you double the dimensions (p), then the area increases by a factor of 4 (q).

Option D, ~q → ~p, is correct as it represents the converse of the original conditional statement. If the area does not increase by a factor of 4 (~q), then the dimensions were not doubled (~p).

The inverse and contrapositive of the original statement are not listed in the given options, so options B, C, and E are not correct representations of the statement's logical structure.