Exercises in Translation and Proof Construction

Symbolic Logic I

Exercises in Translation and Proof Construction

1. If the PLO negotiates or Israel withdraws from the West Bank, then the Mubarak government will fall. But if the U.S. intervenes, then Syria will lose face in the region. Since Syria won't lose face in the region or the Mubarak government won't fall, either the U.S. won't intervene or the PLO won't negotiate and Israel won't withdraw from the West Bank. (P,I,M,U,S,)

2. If CALDWELL is the Russian spy, then somehow he is getting information DIRECTLY out of the lab building to the Russian embassy downtown. He could not make such a direct transmission of information without either BROADCASTING electronically from within the lab or passing the information on MICROFILM through security mail. If Caldwell had made internal broadcasts, then the Security Chief's LOG would show Caldwell's code. Caldwell's code would appear on the SCREENING file, if he had used security mail for microfilm. But his code does not appear either in the screening file or the Security Chief's log. So Caldwell is not the Russian spy.

3. Morality is relative. If morality is relative, nothing is morally wrong. If the Nazis' attempt to destroy the Jewish race is to be condemned, then there are, indeed, actions which are morally wrong. Thus the Nazi attempt to destroy the Jewish race is not to be condemned. (R, W, N)

4. The AWACS will not be of any use to Saudi Arabia unless it doesn't require sophisticated personnel. The Saudis will want to buy the AWACS only if it is truly the product of advanced communications and military engineering. If the AWACS is truly the product of advanced communications and weapons engineering, it must be operated by sophisticated personnel. Therefore, if the AWACS is of any use to Saudi Arabia, the Saudis will not want to buy it. (U, S, W, P)

5. If the South or the North Gate is open, then either the Watchman is intoxicated or the King's Guard is about to leave the city. Whenever the King's Guard is about to leave the city, the Red Flag is flying above the West Tower. Whenever the Watchman is intoxicated, the sound of his bagpipes is heard throughout the city. But the Red Flag is not flying above the West Tower and there is only silence in the air. So, the South and North Gates are both shut.

6. If John has succeeded in traveling backwards in time (as you suggest), he has arrived at his destination both before and after his departure. But his arrival cannot have taken place both before and after his departure. (It's one or the other, not both.) Time travel is in fact possible, only if John has successfully traveled backwards in time. Therefore, time travel is not possible.