Question

use the
$p\to q$
if you are climbing a mountain at an
altitude of 28,500 feet or higher, then
you are on the tallest mountain
above sea level on earth.
$p\to q$ is true.
if you are on the tallest
above sea level on earth,
are on mount everes
$q\to r$ is true.
$p\to r$
if you are climbing a mountain at an altitude of
28,500 feet or higher, then you are on mount everest.
$p\to r$ is true by the law of syllogism.
$p\to r$: if you are climbing a mountain at
an altitude of 28,500 feet or higher,
then you are on mount everest.
$q$: you are climbing a mountain at
an altitude of 28,500 feet or higher.
by the law of detachment, the conclusion $r$ is true
you are on mount everest.
~ independent practice ( try on your ow
try it! 4. if a quadrilateral has four right angles, then it is a rectangle.
if a quadrilateral is a rectangle, then it has two sets of
parallel sides.
a polygon has four sides and four right angles. using the law
of detachment and the law of syllogism, what conclusion can
you draw?

Explanation:

Step1: Apply Law of Syllogism

Let \(p\): A quadrilateral has four right angles.
Let \(q\): A quadrilateral is a rectangle.
Let \(r\): A quadrilateral has two sets of parallel sides.
We know \(p
ightarrow q\) (If a quadrilateral has four right angles, then it is a rectangle) and \(q
ightarrow r\) (If a quadrilateral is a rectangle, then it has two sets of parallel sides).
By the Law of Syllogism \(p
ightarrow r\) (If a quadrilateral has four right angles, then it has two sets of parallel sides).

Step2: Apply Law of Detachment

The given polygon is a quadrilateral (since it has four sides) and has four right angles (\(p\) is true).
Since \(p
ightarrow r\) is true (from Step 1) and \(p\) (the quadrilateral has four right angles) is true, by the Law of Detachment, \(r\) is true.

Answer:

The polygon has two sets of parallel sides.