Question

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?

A) q represents the original conditional statement.
B) p ~q represents the inverse of the original conditional statement.
C) Oq-p represents the original conditional statement.
D) ~ ~ ~p represents the converse of the original conditional statement.

Answer 1

The original conditional statement is represented by q and the converse is represented by ~ ~ ~p.

Step-by-step explanation:

The correct statements are:

A) q represents the original conditional statement.

D) ~ ~ ~p represents the converse of the original conditional statement.

To understand why, let's break down the problem. Doubling the dimensions of a rectangle increases the area by a factor of 4. This means that if the original area is A, the new area after doubling the dimensions is 4A. We can represent this as the statement p: doubling the dimensions of a rectangle and q: the area increasing by a factor of 4. The original conditional statement, which is represented by q, is true, so option A is correct. The converse of the original conditional statement, represented by ~ ~ ~p, is also true, so option D is correct.