Question

select all the correct answers.
if a figure is a rectangle, it is a parallelogram.
p: a figure is a rectangle.
q: a figure is a parallelogram.
which represents the inverse of this statement? is the inverse true or false?
$sim p
ightarrow sim q$
$p leftarrow q$
the inverse of the statement is sometimes true and sometimes false.
$q
ightarrow p$
the inverse of the statement is true.
$sim q leftrightarrow sim p$
the inverse of the statement is false.

Explanation:

Step1: Define inverse of implication

For an implication \(p
ightarrow q\), the inverse is \(\sim p
ightarrow \sim q\).

Step2: Evaluate inverse truth value

\(\sim p\) = "A figure is not a rectangle"; \(\sim q\) = "A figure is not a parallelogram". A rhombus is not a rectangle (\(\sim p\) true) but is a parallelogram (\(\sim q\) false), so \(\sim p
ightarrow \sim q\) is false.

Answer:

$\sim p
ightarrow \sim q$
The inverse of the statement is false.