- If either Algebra is required or Geometry is required, then all students will study mathematics. Algebra is required and trigonometry is required. Therefore, all students will study mathematics. (A, G, S, T)
- Either Smith attended the meeting or Smith was not invited to the meeting. If the directors wanted Smith at the meeting, then Smith was invited to the meeting. Smith did not attend the meeting. If the directors did not want Smith at the meeting and Smith was not invited to the meeting, then Smith is on his way out of the company. Therefore, Smith was on his way out of the company. (A, I, D, W)
- If a scarcity of commodities develops, then prices rise. If there is a change of administration, then fiscal controls will not be continued. If the threat of inflation persists, then fiscal controls will be continued. If there is overproduction, then prices do not rise. Either there is overproduction or there is a change of administration. Therefore, either scarcity of commodities does not develop or the threat of inflation does not persist. (S, P, C, F, I, O)
- If the investigation continues, then new evidence is brought to light. If new evidence is brought to light, then several leading citizens are implicated. If several leading citizens are implicated, then newspapers stop publicizing the case. If continuation of the investigation implies that the newspapers stop publicizing the case, then the bringing to light of the new evidence implies that the investigation continues. The investigation does not continue. Therefore, new evidence is not brought to light. (C, N, I, S)
- If the king does not castle and the pawn advances, then either the bishop is blocked or the rook is pinned. If the king does not castle, then if the bishop is blocked, then the game is a draw. Either the king castles or if the rook is pinned, then the exchange is lost. The king does not castle and the pawn advances. Therefore, either the game is a draw or the exchange is lost. (K, P, B, R, D, E)
- If Andrews is present, then brown is present, and if Brown is present, then Cohen is not present. If Cohen is present, then Davis is not present. If Brown is present, then Emerson is present. If Davis is not present, then Farley is present. Either Emerson is not present or Farley is not present. Therefore, either Andrews is not present or Cohen is not present. (A, B, C, D, E, F)
- Democracy can survive only if people can be taught to work for the public good rather than for their own self-interest. People can be taught to work for public good rather than for their own self-interest only if the theory of psychological egoism is false. Therefore, democracy can survive only if the theory of psychological egoism is false. (D, P, T)
- If either George enrolls or Harry enrolls, then Ira does not enroll. Either Ira enrolls or Harry enrolls. If either Harry enrolls or George does not enroll, then Jim enrolls. George enrolls. Therefore, either Jim enrolls or Harry does not enroll. (G, H, I, J)
- If Tom received the message, then Tom took the plane, but if Tom did not take the plane, then Tom missed the meeting. If Tom missed the meeting, then Dave was elected to the board, but if Dave was elected to the board, then Tom received the message. If either Tom did not miss the meeting or Tom did not receive the message, then either Tom did not take the plane or Dave was not elected to the board. Tom did not miss the meeting. Therefore, either Tom did not receive the message or Tom did not miss the meeting. (R, P, M, D)
- If the fact that the airship Albatros had powerful weapon meant it could destroy objects on the ground, and its capability of destroying objects on the ground meant that the captain could enforce his will all over the earth, then the captain either had good motives for controlling the world or his motives were evil. The airship Albatros had powerful weapon only if its captain had more advanced scientific knowledge than his contemporaries; and if the captain had more advanced scientific knowledge than his contemporaries, then Albatros could destroy objects on the ground. It is either the case that if the Albatros could destroy objects on the ground its captain could enforce his will all over the earth, or it is the case that if he attempted to blow up the British vessel then his passengers would recognize the hoax. It is not the case that his attempt to Blow up the British vessel resulted in his passengers’ recognizing the hoax. Furthermore, the captain’s motives for controlling the world were not evil. Therefore, his motives were good. (A, D, W, G, E, S, B, P)
- Dialectical materialism is true if and only if economic determinism is true. If dialectical materialism is true if and only if economic determinism is true, then both nature as a whole and economic conditions contain opposing forces. If nature as a whole and economic conditions contain opposing forces, these forces can be expressed as laws. Given that such forces can be expressed as laws, their formulation may be discovered by observing history. Their formulation may be discovered by observing history only if there is progress in history and enough time has elapsed for the pattern to be observable. Hence, Marx claimed, there is progress in history and enough time has elapsed for the pattern to be evident. (D, E, N, C, L, F, P, T)
- If Prof. Sparks is right, then this is the best of all possible worlds. Of course, this is the best of all possible worlds only if the evils it contains are necessary evils. If the evils it contains are necessary evils, this implies the truth of the Principle of Sufficient Reason ⎯ i.e., there is good reason for everything being as it is and not otherwise. If there is good reason for everything being as it is and not otherwise, then there must be good reason for Louie having been kicked out by the baron and for the earthquake having destroyed Lisbon. And if either Louie had not been involved in the Inquisition or had not desired lady Cunnie, then either he would not have wandered over America on foot or he would not have lost the sheep from Eldorado. If he had not wandered over America on foot or had not lost the sheep from Eldorado, then some principle other than the Principle of Sufficient Reason would be required to explain what happens in this world. And no principle other than the Principle of Sufficient Reason is required to explain what happens in this world. If it were not true that either Louie had not been involved in the Inquisition or that he had not desired lady Cunnie, then it would be true that Prof. Sparks is right. Therefore, there must be a good reason for Louie having been kicked out by the baron and for the earthquake having destroyed Lisbon. (P, B, E, R, C, L, I, D, W, S, O)