Geometry Help! Jane line question?

L → M and M → ~J thus L → ~J. Now, L implies both J and ~J, but it is impossible to have both. Thus, we must not have L. This means the line is short (assuming "short" is equivalent to "not long"). We can say nothing about morning or not; it could be any time of day.

There are two possibilities:

1. The line is short in the morning and Jane won't go home.

2. The line is short some other time of day. We can't conclude anything about whether Jane goes home. She could stay or go.

Let's reorganize the pieces and see if the answer falls out:

1. if line is long, Jane goes home

3. If line is long, it's morning

2. if it's morning, Jane won't go home

So if the the line is long, it's morning and Jane goes home (1+3) but Jane can't go home in the morning (2)

Therefore the line must be short in the morning.