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. ( square p \to q ) represents the original conditional statement. ( square sim p \to sim q ) represents the inverse of the original conditional statement. ( square q \to p ) represents the original conditional statement. ( square sim q \to sim p ) represents the converse of the original conditional statement. ( square p \to sim q ) represents the contrapositive of the original conditional statement.

Explanation:

Step1: Analyze the original conditional statement

The original statement is "If \(p\) (doubling the dimensions of a rectangle), then \(q\) (the area increasing by a factor of 4)". So \(p
ightarrow q\) is the original conditional statement.

Step2: Analyze the inverse of the conditional statement

The inverse of \(p
ightarrow q\) is \(\sim p
ightarrow\sim q\) (If not \(p\) (not doubling the dimensions of a rectangle), then not \(q\) (the area not increasing by a factor of 4)).

Answer:

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