$252/$ whenterton to QUANTIFCATION

$9\mathrm{.}18($Translation$)$ Open Leibniz's World. This time, we will translate some sentences while looking at the world they are meant to describe.

Start a new sentence file, and enter translations of the following sentences. Each of the English sentences is true in this world. As you go$,$ check to make sure that your translation is indeed a true sentence.

There are no medium$-$sized cubes.

Nothing is in front of $b.$

Every cube is either in front of or in back of $e.$

No cube is between a and $c.$

Everything is in the same column as $a,b,$ or $c.$

Now let's change the world so that none of the English sentences is true. We can do this as follows. First change $b$ into a medium cube. Next, delete the leftmost tetrahedron and move $b$ to exactly the position just vacated by the late tetrahedron. Finally, add a small cube to the world, locating it exactly where $b$ used to sit. If your answers to $1-5$ are correct, all of the translations should now be false. Verify that they are.

Make various changes to the world, so that some of the English sentences come out true and some come out false. Then check to see that the truth values of your translations track the truth values of the English sentences.