Question

If three points are on the same line, then they are collinear. Points x y and z are on line m. Use law of detachment to make a conclusion. If not explain.

Answer 1

Not sure if this will click for you but here is a rough explanation of Law of Detachment 

1) If you are a penguin, then you live in the Southern Hemisphere.

2) You are a penguin.

Let pp be the statement "you are a penguin", let qq be the statement "you live in the Southern Hemisphere".

Then (1) and (2) can be written

1) If pp , then qq .

2) pp .

So, by the Law of Detachment, we can deduce that qq is true. That is,

You live in the Southern Hemisphere.