### Video Transcript

Hannah knows that the following two
statements are true: If a student does not complete their homework, they will get
detention. If the student gets detention, they
will be late home. Jacob got detention and was late
home. Can we conclude that he did not
complete his homework?

What we have in these two
statements in logic is called the law of syllogism. It goes like this: if p, then q; if
q, then r. Therefore, if p, then r. We go from p to q and from q to
r. And that means logically if event p
happens, then event r will happen.

The key to working correctly with
this logic though is remembering that it doesn’t work in the opposite direction. You can’t start with your
conclusion and then go back to your conditional. These logic statements flow from
left to right and not the other way around.

Jacob got detention and was late
home. Can we conclude that he did not
complete his homework?

Event r happened to Jacob. He was home late. Can we trace that backwards to
event p? Can we say that he did not complete
his homework? No, that’s faulty logic to say
that. The only thing we can say is that
he got detention and was late home. We cannot assume that he did not
complete his homework.

The next statement says, Jennifer
did not do her homework. Event p has occurred: a student did
not complete their homework. Can we conclude that she was late
home?

If event p happens — students don’t
complete their homework — then event q will happen — they will get detention. If students get detention, they
will be late home. And that means yes, absolutely we
can conclude because Jennifer did not do her homework. And it’s true that students who do
not complete their homework get detention. And students who get attention will
be home late. Yes, that is a valid
conclusion.