7.11 (Describing a world) Launch Tarski's World and choose Hide Labels from the Display menu. Then, with the labels hidden, open Montague's World . In this world, each object has a name, and no object has more than one name. Start a new sentence file where you will describe some features of this world. Check each of your sentences to see that it is indeed a sentence and that it is true in this world. 1. Notice that if c is a tetrahedron, then a is not a tetrahedron. (Remember, in this world each object has exactly one name.) Use your first sentence to express this fact. 2. However, note that the same is true of band d. That is, if b is a tetrahedron, then d isn't. Use your second sentence to express this. 3. Finally, observe that if b is a tetrahedron, then cisn't. Express this. 4. Notice that if a is a cube and b is a dodecahedron, then a is to the leftof b. Use your next sentence to express this fact. 5. Use your next sentence to express the fact that if b and c are both cubes, then they are in the same row but not in the same column. 6. Use your next sentence to express the fact that b is a tetrahedron only if it is small. [Check this sentence carefully. If your sentence evaluates as false, then you've got the arrow pointing in the wrong direction.] 7. Next, express the fact that if a and d are both cubes, then one is to the left of the other. [Note: You will need to use a disjunction to express the fact that one is to the left of the other.] 8. Notice that d is a cube if and only if it is either mediumor large. Express this. 9. Observe that if b is neither to the right nor left of d, then one of them is a tetrahedron. Express this observation. 10. Finally, express the fact that band care the same size if and only if one is a tetrahedron and the other is a dodecahedron. Save your sentences as Sentences 7.11 . Now choose Show Labels from the Display menu. Verify that all of your sentences are indeed true. When verifying the first three, pay particular attention to the truth values of the various constituents. Notice that sometimes the conditional has a false antecedent and sometimes a true consequent. What it never has is a true antecedent and a false consequent. In each ofthese three cases, play the game committed to true. Make sure you understand why the game proceeds as it does