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? choose two correct answers. p→~q represents the contrapositive of the original conditional statement. ~p→~q represents the inverse of the original conditional statement. p→q represents the original conditional statement. ~q→~p represents the converse of the original conditional statement. q→p represents the original conditional statement.

Explanation:

Step1: Recall conditional - statement forms

For a conditional statement \(p
ightarrow q\), the inverse is \(\sim p
ightarrow\sim q\), the converse is \(q
ightarrow p\), and the contra - positive is \(\sim q
ightarrow\sim p\).
The original statement is "If \(p\) (doubling the dimensions of a rectangle), then \(q\) (the area increasing by a factor of 4)", which is written as \(p
ightarrow q\).

Step2: Analyze each option

• Option 1: \(p

ightarrow\sim q\) is not the contra - positive. The contra - positive of \(p
ightarrow q\) is \(\sim q
ightarrow\sim p\), so this option is false.

• Option 2: \(\sim p

ightarrow\sim q\) is the inverse of \(p
ightarrow q\), so this option is true.

• Option 3: \(p

ightarrow q\) represents the original conditional statement, so this option is true.

• Option 4: \(\sim q

ightarrow\sim p\) is the contra - positive, not the converse. The converse is \(q
ightarrow p\), so this option is false.

• Option 5: \(q

ightarrow p\) is the converse, not the original conditional statement, so this option is false.

Answer:

B. \(\sim p
ightarrow\sim q\) represents the inverse of the original conditional statement.
C. \(p
ightarrow q\) represents the original conditional statement.