Symbolic Logic I
Constructing Proofs
Construct a proof for each of the arguments given below.
1.1.A (B v C) prove D v E
2.A
3.B F
4.~G ~C
5.(F v G) D
2.1.~A ~Bprove B C
2.~A v F
3.~(F ~C)
3.1.A (B ~C)prove ~G
2.F ~A
3.F v B
- G C
4.1.~A v (B C)prove ~I
2.(A C) D
3.~D v (G H)
- H ~I
5 If power is on in the southeast district, then station one or station two is operational and the main station at Hudson Point is also operational. If power is off in the northeast district, then station one is not operational (provided that power is also off in the northwest district. So we know that station two is operational. For we have power in the southeast district, but there is no power in either the northeast or the northwest district.
6. 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.
7. 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.